I was born in New York, New York, on July
31, 1944, the middle child between two sisters, Stephanie and
Vanessa. I grew up in Hastings-on-Hudson, a village of about 8000
outside the city, in a house that Vanessa and her family live in
today. My father, born in Philadelphia the son of immigrant
parents, was a professor of sociology at Columbia
University. He is now University Professor Emeritus at
Columbia, having meanwhile been awarded the National Medal of
Science for founding the sociology of science and for his
contributions to sociological knowledge such as the
self-fulfilling prophecy and the focus group. My mother, from a
multigenerational southern New Jersey Methodist/Quaker family,
stayed at home. She died in 1992. My mother's mother and many (at
one time 25) cats completed the household that shared my
childhood.
Hastings was a mixed middle-class and blue-collar town with local
employment dominated by a wire and cable company and a chemical
plant. Despite this composition and the town's small size, the
local public school provided a fine education opportunity. In a
graduating class of only some 90, I nevertheless was able to take
mathematics through the calculus and five years of science (two
in physics including a MIT-designed course). I was a good student
but not at the top of my class. I played varsity football and ran
track, neither with great distinction. Among my classmates were
the sons of the Columbia physicists and Nobel laureates, James Rainwater and
Jack
Steinberger. Other long-time Hastings residents were the
laureate in medicine, Max Theiler, and the
laureate in economics, William
Vickrey, as well as the sculptor Jacques Lipchitz.
School work and intellectual interests such as music and the arts
were not especially important to me while I was growing up,
although mathematics, my favorite subject, was fun. Baseball was
my first passion: I played sand lot and Little League, and rooted
for the Brooklyn Dodgers. Around age 11, that passion began to
turn toward cars. On my bedroom wall, I put a large sheet of
paper with 1800-plus numbers: one to be crossed out each day
until I would be old enough for my driver's license. As I had
known all the batting averages and pitching records of big league
baseball players, so I came to know the horsepower, cubic inches
of engines size, and other detailed specifications of just about
every automobile in the post-war era. Going to auto shows and
stock car races and handing tools to older, amateur buffs working
on their cars were outlets for my passion until, at age 15, I
bought and rebuilt my first car. After getting my driver's
license, I built street hot rods which I raced at drag strips in
upstate New York and Long Island. I thought that I would become
an automobile engineer when I grew up. Indeed, while in college,
I spent two summers working for Ford in its headquarters in
Dearborn, Michigan: one as an engineer in advanced vehicle design
and the other in the Lincoln-Mercury division trying to figure
out optimal importing patterns for the English Ford. Other than
working in a local cemetery after school and in the summer during
high school and a summer spent in information technology at IBM,
these automotive jobs were the only full-time, non-academic ones
I have had.
Both of my parents played important roles in my early life of
learning. My father introduced me to baseball, poker, magic, and
the stock market (only magic didn't take root). And books of
every kind were everywhere. He said nothing directly about
expected academic performance. There was no need to. Simply by
self-exemplification, he set the standards for work effort and
for clarity of thought and expression. I had the normal
father-son tensions as a teenager, but we subsequently became
very close: for more than 30 years, we have talked to each other,
at least once, nearly every day. My mother taught me caring and
sensitivity towards the feelings of others, animals as well as
humans. She gave me much good, practical advice for getting
through life. One such counsel in particular I have applied often
and in varied arenas: "First show them that you can do it their
way, so that you earn the right to do it your way."
One week before my 17th birthday, I had a blind date with June
Rose, a television actress on network soap operas, a model, and a
regular on the popular Dick Clark's Saturday night American
Bandstand show from New York. We were married five years later,
one week after my graduation from Columbia. We devoted much
energy to and derived enormous pleasure from raising three
wonderful and talented children, Samantha J., Robert F., and Paul
J. June and I separated in 1996.
My arrival at college marked the beginning of serious focus on
academic matters. Just one day after entering Columbia College I
switched to the Engineering School. With its small and flexible
program and fine faculty, it was a great place for an
undergraduate to explore mathematics and its uses. I took several
undergraduate and graduate mathematics courses, both applied and
pure: my tastes were however clear, preferring partial
differential equations to real analysis and the calculus of
variations to functions of a complex variable. Along with a
number of engineering courses including drawing, I also took
Columbia's famous Contemporary Civilization course, humanities,
one introductory course in economics (using Samuelson's
Economics), a graduate course in mathematical sociology,
and two general studies night courses in accounting and stock
market investments. The C- or D received in my English literature
course in my sophomore year did not help my grade point average.
The paper onGulliver's Travels written for that course,
however, became my first published article (in the Journal of
the History of Ideas).
After Columbia, I went west to pursue a Ph.D. in applied
mathematics at the California Institute of Technology. My time at Cal
Tech (1966-67), brief as it was, added significantly to my stock
of mathematics. Even more valuable to me was its creed of placing
students from the outset in a research framework, "playing" with
their subject instead of merely passively learning the material.
Sometime during the year, I decided to leave Cal Tech (and
mathematics) to study economics. Although he thought it was a
bizarre idea, Gerald Whitham (the department head) provided
generous help. I applied to half a dozen good departments, but
only one, M.I.T., accepted me, and it gave me a full
fellowship.
My decision to leave applied mathematics for economics was in
part tied to the widely-held popular belief in the 1960s that
macroeconomics had made fundamental inroads into controlling
business cycles and stopping dysfunctional unemployment and
inflation. Thus, I felt that working in economics could "really
matter" and that potentially one could affect millions of people.
I also believed that my mathematics and engineering training
might give me some advantage in analyzing complex situations.
Most important in my decision was the sense that I had a much
better intuition and "feel" into economic matters than physical
ones. Nowhere was that more apparent to me than in the stock
market.
As early as 8 or 9 years of age, I developed an interest in money
and finance, even at play. I created fictitious banks such as the
RCM Savings of Dollars and Cents Company. I gladly balanced my
mother's check book. As already noted, my father introduced me to
the stock market. At 10 or 11, I drew up an "A" list of stocks,
and bought my first one, General Motors. In college, I spent time
doing some trading, learning tape watching, and hearing the lore
of the market from retail traders in brokerage houses. In late
1963, I had my first experience in what is now known as "risk
arbitrage". The trade surrounding the merger of Friden Company
and Singer Company involved buying Friden shares and shorting
Singer shares in a ratio of 1.75-to-1. The current difference in
value between the two would become a "sure-thing" profit,
provided the merger went through. Fortunately for me, it did. At
Cal Tech, many mornings I would get to a local brokerage house at
6:30 am (9:30 am in New York) for the opening of the stock
market, spend a couple of hours watching the tape and trading,
and then go to my classes. In addition to stocks, I traded
warrants, convertible bonds, and over-the-counter options.
Although I did apply mathematical skills, my valuation approaches
were essentially ad hoc. Nevertheless, I learned much from
those varied transactional experiences about markets and
institutions which proved useful in my later research. For
instance, in discovering specialized banks that would legally
finance my convertible bond positions at 85 percent of their
value (leveraging terms considerably superior to the 50 percent
financing offered by standard margin accounts), I learned early
on that the "institutional rigidities," often postulated as
inviolate in academic financial-market modeling, can be more
flexible and permeable in their real-world counterparts.
When I arrived at MIT in the fall of 1967, I discovered why they
had admitted me when no other institution had: Harold Freeman,
statistician and member of the economics department from
pre-Samuelson days. Harold had recognized some of the
mathematicians who had written my letters of recommendation and
convinced the department to take a flyer. Now in the role of
first-year advisor, he saw my proposed, "traditional" course plan
and told me "...you follow that and you'll leave here by the end
of the term out of boredom ... go take Paul Samuelson's mathematical economics
course." I did. Not only did I get to interact with Paul
Samuelson, but I met the then second-year students, Stanley
Fischer and Michael Rothschild. I learned economics from Paul's
Foundations and wrote a term paper on an optimal growth
model with endogenous population changes which was later
published in 1969. As a result of our meeting in his course, Paul
hired me as his research assistant that spring. Quite a yield
from a single course!
In the course of my work for Paul, we discovered shared interests
and some common knowledge about the stock market, warrants and
convertible securities. I found out that my "after/before-hours"
interest in such things could also be a legitimate part of my
day-hours devoted to research. In the summer of 1968, we began a
joint effort to advance Paul's 1965 theory of warrant pricing,
which was subsequently published in 1969. Later in October, I
would have my first experience presenting in a formal seminar. My
co-author decided that I, the second-year grad student, and not
he, the Institute Professor, would give our paper at the
inaugural session of the MIT-Harvard
Mathematical Economics seminar. With a full audience of Harvard
economics faculty including Kenneth
Arrow, Wassily Leontief, and
Hendrik Houthakker, it was surely a memorable baptism.
The research with Paul on warrant pricing introduced me to the
expected utility maxim and its application to optimal portfolio
selection in a static framework. As a consequence of that effort,
I began to think about combining the static theory of portfolio
selection with the intertemporal optimization of lifetime
consumption under certainty found in the growth-model literature.
Ignorant of the important work underway by Nils Hakansson and
Hayne Leland, then graduate students elsewhere, I attacked the
problem of dynamic portfolio theory in a continuous-time
framework without having the benefit of their discrete-time
formulations. Despite all the mathematics courses that I had
taken, l had seen neither stochastic dynamic programming nor the
Ito calculus, both of which turned out to be key mathematical
tools needed for this research. Instead, driven by "need," I
found them and learned them on my own. Presented first at a
Harvard-MIT graduate student seminar in November 1968, my paper
on lifetime consumption and portfolio selection under uncertainty
was published the following August as a companion paper to one by
Paul investigating the effect of age on portfolio risk
tolerance.
Despite having Paul Samuelson, Franco Modigliani, Robert Solow, Frank Fisher, Robert
Bishop, Evsey Domar, Peter Diamond, Peter Temin, and Ed Kuh as
teachers, I must confess that my focus was more on research than
classes from the beginning (and my course grades reflected that).
However, no one could have had a better introduction to economics
than I did, with these great teachers and the opportunity to live
in Paul Samuelson's office as his assistant for two and a half
years. Three of the five chapters of my thesis were published
before the thesis was submitted. A fourth, "Optimum Consumption
and Portfolio Rules in a Continuous-Time Model," was presented at
the Second World Congress of the Econometric Society in August
1970 and was published in 1971. During those most productive days
of graduate study, I also developed much of my 1970 working paper
on equilibrium asset pricing and the pricing of the capital
structure of the firm which formed the core of my later papers on
the intertemporal capital asset pricing model, the rational
theory of option pricing, and the pricing of corporate
debt.
Paul nominated me to be a Junior Fellow at Harvard. After being
rejected, however, I had no choice but to get a job. I spent the
fall and winter of 1969 interviewing only with departments of
economics, but I ended up taking an appointment to teach finance
at M.I.T.'s Sloan School of Management. It was Franco Modigliani,
with a foot in both the department and Sloan, who made the
invitation and who convinced me that I could teach there even
though I had no formal training in finance. I had been a student
of Franco's and my research on optimal lifetime consumption and
portfolio selection supported his Life-Cycle Hypothesis. Our
relationship, however, became even stronger in the years after I
joined Sloan. I was especially honored and greatly touched when
he invited me to be the speaker at the traditional American
Economics Association luncheon honoring him for receiving the
1985 Nobel Prize. That occasion (the remarks later published in
Economic Perspectives) provided the opportunity to
express, albeit inadequately, the deep respect and affection I
hold for Franco. Some years later, he made a physically very
demanding trip to Rome specifically to be the speaker at the
National Academy
of Lincei on the occasion celebrating my receiving the
International INA-Accademia Nazionale dei Lincei Prize.
It was in the process of interviewing for the job at Sloan that I
met Myron Scholes, a recent arrival to the faculty from the
University of
Chicago. As I note in the accompanying lecture, the story of
my meeting Myron Scholes and Fischer Black and our subsequent
interactions and collaborations are well described in Myron's
Nobel Lecture, in our joint tribute in memory of Fischer Black,
in Fischer's own writings, and in the book by Peter Bernstein.
Thus, even with its obvious central importance to my professional
life, both its academic and practitioner parts, there is no need
to repeat it here.
When I joined the finance group at M.I.T., the faculty consisted
of assistant professors Myron Scholes, Stewart Myers, and Gerry
Pogue and senior professors Daniel Holland and Franco Modigliani.
Dan specialized in tax matters and Franco was involved in many
things everywhere. As a consequence, de facto, the junior
faculty "ran" everything in the group with respect to both
teaching and research. It was a wonderful environment of benign
neglect in which all of us could grow. I enjoyed teaching from
the start. My first experience was in 1969 as one of four
graduate students (Karen Johnson, David Scheffman, and Jeremy
Siegel were the others) who team-taught the second monetary
course usually taught by Paul Samuelson. I began, however,
full-time teaching at Sloan in the fall of 1970 with two regular
courses in the Master's degree program in management: general
finance and advanced capital markets. In the basic course
involving both capital markets and corporate finance, I taught
Markowitz-Tobin portfolio
theory, the Sharpe(-Lintner-Mossin)
Capital Asset Pricing Model, and the Modigliani-Miller theorems,
learning much of the material barely before I presented it to the
students. For my own sense of security and to provide some
evidence of preparation to the students, I gave them detailed
(handwritten) teaching notes for each class. Lecturing from them
saved me from having to write everything down on the blackboard
and saved the students from having to copy what I would have
otherwise written. This in turn left more time for in-class
discussion. These notes became so popular that I prepared similar
ones for every course I taught at Sloan, long after I had learned
the subject matter. In the capital markets course that first
year, I introduced intertemporal portfolio selection,
Black-Scholes type option pricing and hedging and its application
to the pricing of corporate liabilities. I did so not as an
"outlet" for presenting my research interests but because I
thought that the training would be quite useful in practice. I
believed that teaching this material, even before it was
published, was more important for the M.S. students than for the
Ph.D. students since non-academic jobs were not likely to provide
the same opportunity as academics to keep up with the research
literature after graduation. At Sloan in those days, M.S. and
Ph.D. students in finance took the same courses, and so both
groups were exposed to this research long before its
publication.
Throughout the 18 years I spent at the Sloan School, it was a
stimulating and happy place to do research. I shall always owe a
great debt to my brilliant colleagues there: Myron Scholes and
Fischer Black, Franco Modigliani, Stewart Myers, John Cox, Chi-fu
Huang, Terry Marsh, Richard Ruback, Douglas Breeden
(unfortunately, only as a visitor), and from the Economics
Department, Stanley Fischer and Paul Samuelson. The tenure and
the tenor of the finance area varied considerably and it was
small, rarely having more than a half dozen members at a time.
But the quality of mind, diversity of thought, devotion to the
subject of finance, and genuine affection for one another were
reliable constants throughout those years.
I see my research interests as fitting into three regimes of
roughly equal lengths across time: 1968 to 1977, 1977 to 1987,
and 1988 to the present, with a reflective year 1987-1988. The
first period was my most productive one for basic research, in
terms of both the number of papers produced and the originality
and significance of contribution. The central modeling theme was
continuous-time stochastic processes with
continuous-decision-making by agents. Locating this modeling
approach within mathematical economics, I see my models falling
in the middle range between simple models (e.g., one or
two-periods with a representative agent) designed to give
insights (associated by some with the "M.I.T. School") and full
general equilibrium models on a grand scale involving an
arbitrary number of agents with general preferences and
production technologies (often associated with the "Berkeley
School"). Compared with discrete-time dynamic formulations, the
continuous-time models are mathematically more complex. But by
explicitly setting the trading interval and modeling the
evolution of the system as diffusion processes, the derived
results of the continuous-time models were often more precise and
easier to interpret than their discrete-time counterparts. As a
consequence, these theoretical models combined enough richness
and tractability to be applied normatively for decisions in
practice and positively in empirical tests. Of course, all models
involve abstractions from complex reality. I see the relative
importance of my contribution to be more in selecting "good"
abstractions than in introducing and applying mathematical
power.
My first decade's research focus on developing dynamic models of
optimal lifetime consumption and portfolio selection, equilibrium
asset pricing, and contingent-claim pricing shifted in the
1978-1987 period to applications of those models. A series of
papers examined the various risk-bearing roles of pay-as-you-go
and funded social security and defined-benefit,
defined-contribution, and integrated private-sector pension
plans. I also applied option-pricing theory to the valuation of
deposit insurance, market-timing information, corporate
investment decisions, and implicit labor contracts. I worked on
models for estimating expected returns on the market portfolio,
for fitting dividend and earnings behavior, and for testing of
investor market-timing skills. A number of papers including my
Presidential address to the American Finance Association examined
the rationality of capital-market prices and the effects of
market imperfections on equilibrium asset prices. With Stanley
Fischer, I also wrote on issues common to macroeconomics and
finance. Others whom I was fortunate to publish with during this
period were Zvi Bodie, Mathew Gladstein, Roy Henriksson, Alan
Marcus, Terry Marsh, Scott Mason and, for the first time, Myron
Scholes. In contrast, during the prior decade, I had had only two
co-authors: (three papers with) Paul Samuelson and (one with)
Marti Subrahmanyam.
In 1987, I took my first-ever sabbatical year to write a book
based on my work in continuous-time finance. Peter Dougherty,
then an editor at Basil Blackwell, had suggested a book nearly a
year before that would use my previously published papers as the
core. As it happened, I had been thinking about putting my ideas
on the subject together and Peter's expressed interest served as
a catalyst. M.I.T. graciously provided my full salary for the
year and the Harvard Business School kindly offered an office in
which to work. It was a most enjoyable and productive time. With
no other commitments, I wrote nearly every day with no limit on
length and no set deadline for either any piece or the whole.
Earlier writings were corrected and, in some cases, significantly
expanded. Five new chapters were created incorporating my
cumulative thoughts in the fields of optimal portfolio selection,
option pricing, financial intermediation, and general equilibrium
theory. I even took pleasure in developing my own extensive index
and bibliography.
This reflective year was a watershed, both for my research and
for where it would take place. In effect, Continuous-Time
Finance was the crowning synthesis of my earlier work. Its
Chapter 14 on intermediation and institutions, however,
represented a bridge to a new direction of my research. From that
time until the present, I have focused on understanding the
financial system with special emphasis on the dynamics of
institutional change. In particular, I am studying the role of
financial technology and innovation in driving changes in
financial institution and market design, the management of
financial-service firms, and the regulatory and the accounting
systems. There is, however, continuity of this line of inquiry
with the past: Fischer's, Myron's and my derivative-security
research provided much of the foundation for the contracting and
security-design technology that is central to the extraordinary
wave of real-world financial innovation of the past two
decades.
My decision to move from M.I.T. to the Harvard Business School in
1988 was significantly influenced by this turn in my research
interests. Although it was a difficult decision to make, I have
never since doubted that it was the right one. Both the
institution and my colleagues have treated me in extraordinary
fashion. A prime exemplifying case: shortly after my joining the
HBS faculty, then-Dean John McArthur resigned from the George
Fisher Baker professorship in order to give it to me. Giving the
name chair of the founding-sponsor of the School-known as the
"Dean's Chair" since the beginning--to a newly arrived professor
of mathematical finance who had not yet taught a single HBS
student, was a towering symbol and statement of confidence and
support. That recognition meant all the more to me because it was
given after I had happily accepted the School's offer and this
timing made it altogether clear that it was not part of any
negotiation. Now, a decade later, I am especially pleased to
become the first John and Natty McArthur University Professor and
to have the Baker chair become once again the "Dean's
Chair."
For nearly a decade, I have enjoyed developing the new work on
the financial system: to begin with, on my own, but then quite
soon after, in a delightful, productive and multi-faceted
collaboration with Zvi Bodie, professor of finance at Boston University, whom
I have known since the early 1970s when he was a student in the
M.I.T. department of economics. Together we have developed the
idea of using a "functional" perspective to analyze and to
predict financial institutional change over time and to provide a
better understanding of contemporaneous institutional differences
across geopolitical borders. Zvi and I have refined and applied
this idea in a series of working papers, published articles, and
book chapters. In 1992, Zvi and my HBS colleague and my former
MIT student, Carliss Baldwin, led the way to the creation of the
Global Financial System project at the Harvard Business School.
The project which involves several of my finance colleagues (and
Zvi) working together with senior management from 15 major global
financial-service firms has considerably expanded the research
effort devoted to applying the functional approach to the
financial system and to the management of financial institutions.
Whether published as jointly or singly authored, my work with Zvi
in this area has always been collaborative. Conceived at the
outset as a parallel development to our research, but completed
only now, is our textbook on basic finance that applies this
perspective and presents the subject as a set of principles much
like first-courses in economics and the physical sciences.
Throughout the last 30 years of academic research, I have been
involved in finance practice. The vast bulk of my research has
been in mathematical finance theory, but I believe that my
involvement in practice has shaped that research and in turn has
been shaped by it, this interplay to the benefit of both. A
targeted instance can be found in the section of my 1973 rational
option pricing paper on pricing and hedging the risk of the
"down-and-out" call option. I became aware of such instruments in
the early 1970s only as a consequence of a consulting assignment
from a firm that was issuing them in Asia. In the decades since,
the down-and-out option has become the prototype example of the
exotic option, which is now a large, mainstream class of
financial-product offerings.
My first consulting experience was in 1969 for a southern
California bank on the pricing of warrants. Ironically, had the
"equal-yield-for-equal sigmarisk" model I developed ad hoc
for them been taken to its continuous-trading limit, it would
have led to the Black-Scholes pricing formula but of course
without any of the rigorous foundation underlying that formula
which includes the key hedging insight of Black and Scholes.
Myron Scholes and I began working together on consulting projects
shortly after I joined the Sloan faculty. In 1972, we were
engaged by Mathew Gladstein of the options department of
Donaldson, Lufkin, & Jenrette to develop option pricing and
hedging models for the over-the-counter market and later for the
new Chicago Board Options Exchange. In 1973, Leo Pomerance, head
of the DLJ options department, became the first chairman of the
CBOE. Myron and I learned much from our DLJ experience and
indeed, our first publications together in 1978 and 1982 evolved
directly from a mutual-fund project which DLJ helped us to
underwrite.
As a consequence of the extraordinary decline in the stock market
in 1973-74, Myron and I had an idea for a mutual-fund product
that would provide significant downside protection to the
investor while at the same time affording significant exposure to
upside movements in the stock market. The strategy designed to do
this was to purchase a diversified portfolio of call options with
10 percent of the assets and to invest the balance of the assets
in short-term money-market instruments, with those proportions
rebalanced every 6 months. Since the strategy involved option
buying instead of option writing, many cautioned us that the SEC
might see it as "too speculative" for the first option-based
mutual fund in the United States and thus, would create serious
roadblocks. They were wrong: the staff of the SEC apparently
understood the fund's relatively conservative design and approved
it with essentially no delays. The strategy was thus implemented
with the creation of Money Market/Options Investment, Inc., an
open-ended mutual fund, which went effective in February 1976.
The portfolio's subsequent performance fit the simulations
projected for it. Nevertheless, and despite being a direct
predecessor to the portfolio-insurance products of the 1980s and
the various successful "floor" products offered around the globe
in the 1990s, MM/OI was not a commercial success. Still, it was
for us a broadening experience about the multi-dimensional
aspects of setting up a new financial entity. As Myron is fond of
observing, "Sometimes the early bird gets the worm ... and
sometimes, it gets frozen."
For the rest of the 1970s and much of 1980s, I kept my hand in
practice, serving on a few mutual fund boards and being elected a
trustee of College Retirement Equities Fund. During the early
1980s, several of my former students from M.I.T., most of them
Ph.D.s, were attracted to Salomon Brothers, the global investment
bank, by John Meriwether and under his leadership, they helped
build an enormously successful proprietary trading group focused
on arbitrage in the fixed-income markets. The core financial
technology used in the group was based on the
Black-Scholes-Merton derivative-security models, but it was
highly refined to take account of much greater empirical detail
and practical market experience. In 1988, one of those former
students, Eric Rosenfeld, and Thomas Strauss, then President of
Salomon, came to see me about becoming a special consultant to
the Office of the Chairman. They made me an offer I couldn't
refuse: unlike the simple model-building/product-design role of
my past consultancies, this one also called for a role as trusted
advisor (with technical skills) to the CEO on business matters of
the firm and on the direction of institutional change in the
global financial system. One could hardly imagine a better fit to
inform, and to be informed by, my then-new direction of research
on the functional perspective. Over the next four years, I
learned much about the operations and management of a global
intermediary, and trust that I contributed something as well. I
definitely strengthened old friendships with former students and
developed new friendships with their colleagues, and Myron and I
got back together in practice when he joined Salomon from
Stanford.
In early 1993, John Meriwether who had left Salomon in 1991, Eric
Rosenfeld who had recently left and James McEntee, former
chairman and cofounder of Carroll-McEntee, the primary
government-bond dealer, and John's long-time friend, had the idea
of building a new firm to undertake fixed-income arbitrage on a
global basis. The thought of working with John and Eric once
again and having a hand in building a large-scale financial firm
from scratch was exciting and I immediately volunteered to help
out.
Over the ensuing months, one at a time, senior members of John's
old group left Salomon and showed up ready to get involved in
what became Long-Term Capital Management (LTCM): Victor Haghani
arrived in the spring; Gregory Hawkins and Myron Scholes
(bringing us back together in practice once again) in the summer;
William Krasker in the fall; and Richard Leahy and Larry
Hilibrand at year end. The last of the founders, David Mullins,
who joined LTCM in late winter, never worked at Salomon. With a
Ph.D. from M.I.T. and 15 years on the finance faculty at Harvard
Business School before going into government service, he
exemplifies the strong M.I.T. and HBS connections among the
founders of LTCM: seven of the eleven founders (and nine of the
current sixteen principals of the firm) were either graduates, or
on their faculties, or both.
This small group of founding principals, together with a few key
early employees, put together and tested the financial,
telecommunication, and computer technologies, hired the
strategists and operations people to run them, designed the
organizational structure of the business, executed the complex
contractual agreements with investors and counterparties, found
and outfitted physical quarters in both the United States and
London, and helped to raise over $1 billion from investors. The
design and development efforts along each of these dimensions
attempted to marry the best of finance theory with the best of
finance practice. It all came together in February 1994 when the
firm began active business. Today, LTCM has 180 employees, a
third office in Tokyo, and its capital has grown
considerably.
It was deliciously intense and exciting to have been a part of
creating LTCM. For making it possible, I will never be able to
adequately express my indebtedness to my extraordinarily talented
LTCM colleagues.
The distinctive LTCM experience from the beginning to the present
characterizes the theme of the productive interaction of finance
theory and finance practice. Indeed, in a twist on the more
familiar version of that theme, the major investment magazine,
Institutional Investor characterized the remarkable
collection of people at LTCM as "The best finance faculty in the
world. "
In long retrospect, unexpected roads happily traveled.
| Personal | |
| Born: | July 31, 1944 New York, New York |
| Address: | Harvard Business School Morgan Hall 397 Soldiers Field Boston, MA 02163 |
| Education | |
| B.S., Columbia University (Engineering Mathematics), 1966 | |
| M.S., California Institute of Technology (Applied Mathematics), 1967 | |
| Ph.D., Massachusetts Institute of Technology (Economics), 1970 | |
| Honorary Degrees | |
| Masters of Arts, Harvard University, 1989 | |
| Doctor of Laws, University of Chicago, 1991 | |
| Prof esseur Honoris Causa, Hautes Etudes Commerciales (Paris), 1995 | |
| Doctoris Honoris Causa, University of Lausanne, 1996 | |
| Doctoris Honoris Causa, University Paris-Dauphine, 1997 | |
| Honorary Doctor, National Sun Yat-sen University, 1998 | |
| Academic Appointments | |
| John and Natty McArthur University Professor, Graduate School of Business Administration, Harvard University, 1998- | |
| George Fisher Baker Professor of Business Administration, Graduate School of Business Administration, Harvard University, 1988-1998 | |
| Invited Professor of Finance, Faculté des Sciences Economiques, Université de Nantes, June 1993 | |
| Visiting Professor of Finance, Graduate School of Business Administration, Harvard University, 1987-1988 | |
| J. C. Penney Professor of Management, A. P. Sloan School of Management, Massachusetts Institute of Technology, 1980-1988 | |
| Assistant Professor of Finance, 1970-73, Associate Professor, 1973-74; | |
| Professor 1974-80, A.P. Sloan School of Management, Massachusetts Institute of Technology | |
| Instructor, Department of Economics, Massachusetts Institute of Technologv, 1969-1970 | |
| Research Assistant to Paul Samuelson, Massachusetts Institute of Technology, 1968-1970 | |
| Other Professional Appointments | |
| Principal, co-founder, Limited Partner, Long-Term Capital Management, L.P. (1993-) | |
| Research Associate, National Bureau of Economic Research, 1979- | |
| Trustee, College Retirement Equities Fund (1988-1996) | |
| Director, Travelers Investment Management Company (1987-1991) | |
| Director, ABT Investment Series (1983-1988) | |
| Director, ABT Utility Income Fund (1982-1988) | |
| Trustee, ABT Growth and Income Trust (1982-1988) | |
| Director, Nova Fund (1980-1988) | |
| Elected Societies and Positions | |
| Member, Tau Beta Pi, Columbia University, 1965 | |
| Member, Sigma Xi, Massachusetts Institute of Technology, 1970 | |
| Director, American Finance Association, 1982-84; 1987-88 | |
| Fellow, Econometric Society, 1983 | |
| Fellow, American Academy of Arts and Sciences, 1986 | |
| President, American Finance Association, 1986 | |
| Vice President, The Society for Financial Studies, 1993-96 | |
| Member, National Academy of Sciences, 1993 | |
| Senior Fellow, International Association of Financial Engineers, 1994 | |
| Fellow, Institute for Quantitative Research in Finance ("Q Group"), 1997 | |
| Honorary Member, the Bachelier Finance Society, 1997 | |
| Awards | |
| 1964 | Faculty Scholar Award, Columbia University |
| 1971-72 | Salgo-Noren Award for Excellence in Teaching, Massachusett Institute of Technology |
| 1977-78 | Graduate Student Council Teaching Award, Massachusetts Institute of Technology |
| 1983 | Leo Melamed Prize, University of Chicago |
| 1985, 1986 | First Prize, Roger Murray Prize Competition, Institute for Quantitative Research in Finance |
| 1989 | Distinguished Scholar Award, Eastern Finance Association |
| 1993 | International INA - Accademia Nazionale dei Lincei Prize National Academy of Lincei, Rome |
| 1993 | FORCE Award for Financial Innovation, Fuqua School of Business, Duke University |
| 1993 | Financial Engineer of the Year Award, International Association of Financial Engineers |
| 1997 | The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel |
| 1998 | Inducted, Derivatives Hall of Fame, Derivatives Strategy |
| Selected Lectures | |
| 1975 | Distinguished Speaker Lecture, Western Finance Association |
| 1985 | Mortimer Hess Memorial Lecture, Association of the Bar of the City of New York |
| 1988 | 12th Annual Lecture, Geneva Association, Paris |
| 1992 | Scholl Chair in Finance Distinguished Speaker Lecture, DePaul University |
| 1993 | Lecture, Discussion Meeting on Mathematical Finance, The Royal Society, London |
| 1993 | Keynote, 10th International Conference in Finance, Association Française de France |
| 1994 | AEA/AFA Speaker, Allied Social Sciences Meetings |
| 1994 | Speaker, International Monetary Conference, London |
| 1995 | Lecture, Newton Institute Seminar, Isaac Newton Institute for Mathematical Sciences, Cambridge |
| 1995 | Keynote, 12th International Conference in Finance, Association Française de France |
| 1995 | Keynote, 25th Anniversary, Financial Management Association |
| 1996 | Oxford University Press and Massachusetts Institute of Technology, Sloan School of Management Distinguished Lectures in Business, Massachusetts Institute of Technology, Cambridge |
| 1996 | Donor's Lecture, London Business School, London |
| 1996 | Inaugural, Dean's Research Seminar, Harvard Business School |
| 1996 | Faculty Inaugural Session, University of Lausanne |
| 1996 | Paolo Baffi Lecture on Money and Finance, Bank of Italy, Rome |
| 1997 | Edgar Lorch Memorial Lecture, Sigma Xi, Columbia University |
| 1998 | Lionel McKenzie Lecture, University of Rochester |
| 1998 | Martin H. Crego Lecture, Vassar College |
| 1998 | I.E. Block Community Lecture, Society for Industrial and Applied Mathematics |
| Advisory and Editorial Boards | |
| Current: | |
| International Board of Scientific Advisers, Tinbergen Institute (1995-) | |
| Advisory Board, Brookings-Wharton (1997-) | |
| Advisory Board, International Journal of Theoretical & Applied Finance (1997-) | |
| Advisory Board, Center for Global Management and Research, George Washington University (1996-) | |
| Advisory Board, European Finance Review (1997-) | |
| Advisory Board, Journal of Financial Education (1995-) | |
| Advisory Board, Review of Derivatives Research (1993-) | |
| Advisory Board, Japan Financial Economics Association (1993-) | |
| Advisory Board, Mathematical Finance (1989-) | |
| Editorial Board, Finance India (1988-) | |
| Associate Editor, Journal of Fixed Income (1991-) | |
| Associate Editor, Journal of Banking and Finance (1977-1979, 1992-) | |
| Past: | |
| Advisory Board, The New Palgrave Dictionary of Money and Finance (1989-1992) | |
| Selection Editor, Papers and Proceedings, Journal of Finance, July 1986 | |
| Co-Editor, Journal of Financial Economics (1974-1977) | |
| Associate Editor, Financial Review (1992-1997) | |
| Associate Editor, Geneva Papers on Risk and Insurance (1989-1996) | |
| Associate Editor, Journal of Financial Economics (1977-1983) | |
| Associate Editor, Journal of Money, Credit and Banking (1974-1979) | |
| Associate Editor, Journal of Finance (1973-1977) | |
| Associate Editor, International Economic Review (1972-1977) | |
| Founding Committee, Review of Financial Studies (1986) | |
| Publications, Cases and Unpublished Papers | |
| Books | |
| Finance, with Zvi Bodie, New Jersey: Prentice-Hall, 1998. | |
| The Global Financial System: A Functional Perspective, with D. Crane, K. Froot, S. Mason, A. Perold, Z. Bodie, E. Sirri, and P. Tufano, Boston: Harvard Business School Press, 1995. | |
| Cases in Financial Engineering: Applied Studies of Financial Innovation, with S. Mason, A.F. Perold, and P. Tufano, Prentice-Hall, 1995. | |
| Continuous-Time Finance, Basil Blackwell, Inc. 1990; Revised Edition 1992. | |
| The Collected Scientific Papers of Paul A. Samuelson Volume III, editor, Cambridge, MIT Press 1972. | |
| Published Papers | |
| "The Global Financial System Project," with P. Tufano, in T.K. McCraw, ed., Intellectual Venture Capital: Essays in Honor of Dean John H. McArthur, Boston: Harvard Business School Press, forthcoming 1998. | |
| "Applications of Option-Pricing Theory: Twenty-Five Years Later," Les Prix Nobel 1997, Stockholm: Nobel Foundation. | |
| "Foreword," Mathematics of Derivative Securities, M. A. H. Dempster and S. Pliska, eds., Cambridge University Press, 1997. | |
| "A Model of Contract Guarantees for Credit-Sensitive, Opaque Financial Intermediaries," European Finance Review, Vol. 1, No. 1, 1997, pp. 1-13. | |
| "On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios," in D. Jerison, I. M. Singer, and D. W. Stroock, eds., The Legacy of Norbert Wiener: A Centennial Symposium, PSPM Series, Vol. 60, Providence, RI: American Mathematical Society, 1997. | |
| "Foreword," Managing Derivative Risks, L. Chew, Chichester: John Wiley & Sons, 1996. | |
| "Fischer Black," with M. Scholes, Journal of Finance, 50, December 1995. | |
| "A Functional Perspective of Financial Intermediation," Financial Management, Volume 24, Summer 1995. | |
| "Financial Innovation and the Management and Regulation of Financial Institutions," Journal of Banking and Finance, 19, July 1995. | |
| "Mark-to-Market Accounting for Banks and Thrifts: Lessons from the Danish Experience," with V. Bernard and K. Palepu, Journal of Accounting Research, 33, 1, Spring 1995. | |
| "Influence of Mathematical Models in Finance on Practice: Past, Present and Future," Philosophical Transactions of the Royal Society of London, Series A, Volume 347, June 1994. Reprinted in Financial Practice and Education, Spring 1995. | |
| "Pension Benefit Guarantees in the United States: A Functional Analysis," with Z. Bodie in R. Schmitt, ed., The Future of Pensions in the United States, Pension Research Council, Philadelphia: University of Pennsylvania Press, 1993. | |
| "Theory of Risk Capital in Financial Firms," with A. Perold, Journal of Applied Corporate Finance, Fall 1993. | |
| "Management of Risk Capital in Financial Firms," with A. Perold, in S.L. Hayes III, ed., Financial Services: Perspectives and Challenges, Boston: Harvard Business School Press 1993. | |
| "Deposit Insurance Reform: A Functional Approach," with Z. Bodie, in A. Meltzer and C. Plosser, eds., Carnegie-Rochester Conference Series on Public Policy, Volume 38, June 1993. | |
| "Operation and Regulation in Financial Intermediation: A Functional Perspective," in P. Englund, ed., Operation and Regulation of Financial Markets, Stockholm: The Economic Council 1993. | |
| "Optimal Investment Strategies for University Endowment Funds," in C. Clotfelter and M. Rothschild, eds., Studies of Supply and Demand in Higher Education, Chicago: University of Chicago Press 1993. Chapter 21 in Continuous-Time Finance. | |
| "On the Management of Financial Guarantees," with Z. Bodie, Financial Management, 21, Winter 1992. | |
| "Labor Supply Flexibility and Portfolio Choice in a Life-Cycle Model," with Z. Bodie and W. Samuelson, Journal of Economic Dynamics and Control, 16, July/October 1992. | |
| "Financial Innovation and Economic Performance," Journal of Applied Corporate Finance, Winter 1992. | |
| "The Financial System and Economic Performance," Journal of Financial Services Research, 4, December 1990. | |
| "Capital Market Theory and the Pricing of Financial Securities," in B. Friedman and F. Hahn, eds., Handbook of Monetary Economics, Amsterdam: North-Holland 1990. | |
| "The Changing Nature of Debt and Equity: A Discussion," in R. W. Kopeke and E. S. Rosengren, eds., Are the Distinctions Between Debt and Equity Disappearing? Conference Series #33, Federal Reserve Bank of Boston, 1990. | |
| "On the Application of the Continuous-Time Theory of Finance to Financial Intermediation and Insurance," Twelfth Annual Lecture of the Geneva Association, The Geneva Papers on Risk & Insurance,14, July 1989. | |
| "Options," in The New Palgrave: A Dictionary of Economic Theory and Doctrine, London: MacMillan Press, Ltd. 1987. Revised in The New Palgrave Dictionary of Money and Finance, London: MacMillan Press, Ltd. 1992. | |
| "Continuous-Time Stochastic Models," in The New Palgrave: A Dictionary of Economic Theory and Doctrine, London: MacMillan Press, Ltd. 1987. Revised in The New Palgrave Dictionary of Money and Finance, London: MacMillan Press, Ltd. 1992. | |
| "In Honor of Nobel Laureate, Franco Modigliani," Economic Perspectives,1, Fall 1987. | |
| "Defined Benefit Versus Defined Contribution pension Plans: What Are the Real Tradeoffs?" with Z. Bodie and A. J. Marcus in Pensions in the U.S. Economy, J. Shoven and D. Wise, eds., Chicago: University of Chicago Press 1987. | |
| "A Simple Model of Capital Market Equilibrium With Incomplete Information," Journal of Finance, 42, July 1987. | |
| "On the Current State of the Stock Market Rationality Hypothesis," in Macroeconomics and Finance: Essays in Honor of Franco Modigliani, R. Dornbusch, S. Fischer and J. Bossons, eds., Cambridge: MIT Press 1987. | |
| "Pension Plan Integration as Insurance Against Social Security Risk," with Z. Bodie and A. J. Marcus, in Issues in Pension Economics, Z. Bodie, J. B. Shoven, and D.A. Wise, eds., Chicago: University of Chicago Press 1987. | |
| "Dividend Behavior for the Aggregate Stock Market," with T. A. Marsh, Journal of Business, 60, January 1987. | |
| "Dividend Variability and Variance Bounds Tests for the Rationality of Stock Market Prices," with T. A. Marsh, American Economic Review, 76, June 1986. | |
| "Implicit Labor Contracts Viewed as Options: A Discussion of 'Insurance Aspects of Pensions'," in Pensions, Labor, and Individual Choice, D. A. Wise, ed., Chicago: University of Chicago Press 1985. | |
| "The Role of Contingent Claims Analysis in Corporate Finance," with S. Mason, in Recent Advances in Corporate Finance, E. I. Altman and M. G. Subrahmanyam, eds., Homewood: Richard D. Irwin 1985. | |
| "Macroeconomics and Finance: The Role of the Stock Market," with S. Fischer, in Essays on Macroeconomic Implications of Financial and Labor Markets and Political Processes, K. Brunner and A. H. Meltzer, eds., Vol. 21 Amsterdam: North-Holland, Autumn 1984. | |
| "On Consumption-Indexed Public Pension Plans," in Financial Aspects of the U.S. Pension System, Z. Bodie and J. Shoven, eds., Chicago: University of Chicago Press 1983. Chapter 18 in Continuous-Time Finance. | |
| "On the Role of Social Security As a Means for Efficient Risk-Bearing in an Economy Where Human Capital Is Not Tradeable," in Financial Aspects of the U.S. Pension System, Z. Bodie and J. Shoven, eds., University of Chicago Press 1983. | |
| "Financial Economics," in Paul Samuelson and Modern Economic Theory, E. C. Brown and R. M. Solow, eds., New York: McGraw-Hill 1983. | |
| "On the Mathematics and Economic Assumptions of Continuous-Time Financial Models," in Financial Economics: Essays in Honor of Paul Cootner, W. F. Sharpe and C. M. Cootner, eds., Englewood Cliffs: Prentice Hall 1982. Chapter 3 in Continuous-Time Finance. | |
| "On the Microeconomic Theory of Investment Under Uncertainty," in Handbook of Mathematical Economics, Volume II, K. Arrow and M. Intriligator, eds., Amsterdam: North-Holland Publishing Company, 1982. | |
| "The Returns and Risk of Alternative Put Option Portfolio Investment Strategies," with M. S. Scholes and M.L. Gladstein, Journal of Business, 55, January 1982. | |
| "On Market Timing and Investment Performance Part II: Statistical Procedures for Evaluating Forecasting Skills," with R.D. Henriksson, Journal of Business, 54, October 1981. | |
| "On Market Timing and Investment Performance Part I: An Equilibrium Theory of Value for Market Forecasts,"Journal of Business, 54, July 1981. | |
| "On Estimating the Expected Return on the Market: An Exploratory Investigation, " Journal of Financial Economics, 8, December 1980. | |
| "Capital Requirements in the Regulation of Financial Intermediaries: A Discussion," in Proceedings, The Regulation of Financial Institutions, Conference Series #21, Federal Reserve Bank of Boston, October 1979. | |
| "On the Cost of Deposit Insurance When There Are Surveillance Costs," Journal of Business, 51, July 1978. Chapter 20 in Continuous-Time Finance. | |
| "The Returns and Risk of Alternative Call Option Portfolio Investment Strategies," with M. S. Scholes and M. L. Gladstein, Journal of Business, 51, April 1978. | |
| "On the Pricing of Contingent Claims and the Modigliani-Miller Theorem," Journal of Financial Economics, 5, November 1977. Chapter 13 in ContinuousTime Finance. | |
| "An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance: An Application of Modern Option Pricing Theory," Journal of Banking and Finance, 1, June 1977. | |
| "A Reexamination of the Capital Asset Pricing Model," in Studies in Risk and Return, J. Bicksler and I. Friend, eds., Cambridge, MA: Ballinger 1977. | |
| "The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns," Journal of Finance, 31, May 1976. | |
| "Option Pricing When Underlying Stock Returns are Discontinuous,"Journal of Financial Economics, 3, January-February 1976. Chapter 9 in Continuous Time Finance. | |
| "Theory of Finance From the Perspective of Continuous Time," Journal of Financial and Quantitative Analysis, 10, November 1975. | |
| "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, 42, July 1975. Chapter 17 in Continuous-Time Finance. | |
| "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, 29, May 1974. Chapter 12 in Continuous-Time Finance. | |
| "Fallacy of the Log-Normal Approximation to Optimal Portfolio Decision Making Over Many Periods," with P. A. Samuelson, Journal of Financial Economics, 1, May 1974. | |
| "Generalized Mean-Variance Tradeoffs for Best Perturbation Corrections to Approximate Portfolio Decisions," with P. A. Samuelson, Journal of Finance, 29, March 1974. | |
| "The Optimality of a Competitive Stock Market," with M. C. Subrahmanyam, Bell Journal of Economics and Management Science, 5, Spring 1974. | |
| "An Intertemporal Capital Asset Pricing Model," Econometrica, 41, September 1973. Chapter 15 in Continuous-Time Finance. | |
| "Book Review: Studies in the Theory of Capital Markets, M. C. Jensen, ed.," Journal of Money, Credit, and Banking, May 1973. | |
| "Theory of Rational Option Pricing," Bell Journal of Economics and Management Science, 4, Spring 1973. Chapter 8 in Continuous-Time Finance. | |
| "The Relationship Between Put and Call Option Prices: Comment," Journal of Finance, 28, March 1973. | |
| "Appendix: Continuous-Time Speculative Processes," in P. A. Samuelson, 'Mathematics of Speculative Price,' SIAM Review, 15, January 1973. | |
| "An Analytical Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, 10, September 1972. | |
| "Optimum Consumption and Portfolio Rules in a Continuous-Time Model," Journal of Economic Theory, 3, December 1971. Chapter 5 in Continuous Time Finance. | |
| "A Golden Golden-Rule for Welfare-Maximization in an Economy With a Varying Population Growth Rate," Western Economic Journal, 4, December 1969. Chapter III of Ph.D. dissertation. | |
| "Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case, " Review of Economics and Statistics, 51, August 1969. Chapter II of Ph.D. dissertation. Chapter 4 in Continuous-Time Finance. | |
| "A Complete Model of Warrant Pricing That Maximizes Utility," with P. A. Samuelson, Industrial Management Review, 10, Winter 1969. Chapter IV of Ph.D. dissertation. Chapter 7 in Continuous-Time Finance. | |
| "The 'Motionless' Motion of Swift's Flying Island," Journal of the History of Ideas, 27, April-June 1966. | |
| Cases and Unpublished Papers | |
| Harrington Financial Group," with A. Moel, Harvard Business School Case #9-297-088, April 1997. | |
| "Smith Breeden Associates: The Equity Plus Fund," with A. Moel, Harvard Business School Case #9-297-089, April 1997. | |
| "Savings and Loans and the Mortgage Markets," with A. Moel, Harvard Business School Case #N9-297-090, February 1997. | |
| "Financial Infrastructure and Public Policy: A Functional Perspective," with Z. Bodie, Harvard Business School, Working Paper #95-064, February 1995. | |
| "The Informational Role of Asset Prices: The Case of Implied Volatility," with Z. Bodie, Harvard Business School, Working Paper #95-063, February 1995. | |
| "A Conceptual Framework for Analyzing the Financial Environment," with Z. Bodie, Harvard Business School, Working Paper #95-062, February 1995. "On the Management of Deposit Insurance and Other Guarantees," with Z. Bodie, Working Paper #92-081, May 1992. | |
| "Pension Reform and Privatization in International Perspective: The Case of Israel," with Z. Bodie, Harvard Business School, Working Paper #92-082, May 1992. Published (in Hebrew), The Economics Quarterly, 152 (August 1992). | |
| "A Framework for the Economic Analysis of Deposit Insurance and Other Guarantees," with Z. Bodie, Harvard Business School, Working Paper #92063, January 1992. | |
| "Optimal Portfolio Rules in Continuous Time When the Nonnegativity Constraint on Consumption is Binding," Harvard Business School, Working Paper #90-042, December 1989. Chapter 6 in Continuous-Time Finance. | |
| "Earnings Variability and Variance Bounds Tests for the Rationality of Stock Market Prices," with T.A. Marsh, MIT Sloan School of Management, Working Paper #1559-84, April 1984. "Aggregate Dividend Behavior and Its Implications for Tests of Stock Market Rationality," with T.A. Marsh, MIT Sloan School of Management, Working Paper#1475-83, September 1983. | |
| "Continuous-Time Portfolio Theory and the Pricing of Contingent Claims," MIT Sloan School of Management, Working Paper, November 1976. | |
| "A Dynamic General Equilibrium Model of the Asset Market and Its Application to the Pricing of the Capital Structure of the Firm," MIT Sloan School of Management, Working Paper #497-70, December 1970. Chapter 11 in Continuous-Time Finance. | |
| "Analytical Optimal Control Theory as Applied to Stochastic and NonStochastic Economics," Ph.D. dissertation, Massachusetts Institute of Technology, September 1970. | |
| "An Empirical Investigation of the Samuelson Rational Warrant Pricing Theory," Chapter V in Ph.D. dissertation, class paper, Massachusetts Institute of Technology, Spring 1969. | |
| "Restrictions on Rational Option Pricing: A Set of Arbitrage Conditions," mimeographed, Massachusetts Institute of Technology, August 1968. | |
From Les Prix Nobel. The Nobel Prizes 1997, Editor Tore Frängsmyr, [Nobel Foundation], Stockholm, 1998
This autobiography/biography was written at the time of the award and later published in the book series Les Prix Nobel/Nobel Lectures. The information is sometimes updated with an addendum submitted by the Laureate. To cite this document, always state the source as shown above.
Copyright © The Nobel Foundation 1997