I was born in Chicago in 1927, the only child of
Morris and Mildred Markowitz who owned a small grocery store. We
lived in a nice apartment, always had enough to eat, and I had my
own room. I never was aware of the Great Depression.

Growing up, I enjoyed baseball and tag football in the nearby
empty lot or the park a few blocks away, and playing the violin
in the high school orchestra. I also enjoyed reading. At first,
my reading material consisted of comic books and adventure
magazines, such as *The Shadow*, in addition to school
assignments. In late grammar school and throughout high school I
enjoyed popular accounts of physics and astronomy. In high school
I also began to read original works of serious philosophers. I
was particularly struck by David Hume's argument that, though we
release a ball a thousand times, and each time, it falls to the
floor, we do not have a necessary proof that it will fall the
thousand-and-first time. I also read *The Origin of Species*
and was moved by Darwin's marshalling of facts and careful
consideration of possible objections.

From high school, I entered the University of
Chicago and took its two year Bachelor's program which
emphasized the reading of original materials where possible.
Everything in the program was interesting, but I was especially
interested in the philosophers we read in a course called OII:
Observation, Interpretation and Integration.

Becoming an economist was not a childhood dream of mine. When I
finished the Bachelor's degree and had to choose an upper
division, I considered the matter for a short while and decided
on Economics. Micro and macro were all very fine, but eventually
it was the "Economics of Uncertainty" which interested me--in
particular, the Von Neumann and Morgenstern and the Marschak
arguments concerning expected utility; the Friedman-Savage
utility function; and L. J. Savage's defense of personal
probability. I had the good fortune to have Friedman, Marschak and Savage among
other great teachers at Chicago. Koopmans' course on activity analysis
with its definition of efficiency and its analysis of efficient
sets was also a crucial part of my education.

At Chicago I was invited to become one of the student members of
the Cowles Commission for Research in Economics. If anyone knows
the Cowles Commission only by it influence on Economic and
Econometric thought, and by the number of Nobel laureates it has
produced, they might imagine it to be some gigantic research
center. In fact it was a small but exciting group, then under the
leadership of its director, T. Koopmans, and its former director,
J. Marschak.

When it was time to choose a topic for my dissertation, a chance
conversation suggested the possibility of applying mathematical
methods to the stock market. I asked Professor Marschak what he
thought. He thought it reasonable, and explained that Alfred
Cowles himself had been interested in such applications. He sent
me to Professor Marshall Ketchum who provided a reading list as a
guide to the financial theory and practice of the day.

The basic concepts of portfolio theory came to me one afternoon
in the library while reading John Burr Williams's *Theory of
Investment Value*. Williams proposed that the value of a stock
should equal the present value of its future dividends. Since
future dividends are uncertain, I interpreted Williams's proposal
to be to value a stock by its expected future dividends. But if
the investor were only interested in expected values of
securities, he or she would only be interested in the expected
value of the portfolio; and to maximize the expected value of a
portfolio one need invest only in a single security. This, I
knew, was not the way investors did or should act. Investors
diversify because they are concerned with risk as well as return.
Variance came to mind as a measure of risk. The fact that
portfolio variance depended on security covariances added to the
plausibility of the approach. Since there were two criteria, risk
and return, it was natural to assume that investors selected from
the set of Pareto optimal risk-return combinations.

I left the University of Chicago and joined the RAND Corporation in
1952. Shortly thereafter, George Dantzig joined RAND. While I did
not work on portfolio theory at RAND, the optimization techniques
I learned from George (beyond his basic simplex algorithm which I
had read on my own) are clearly reflected in my subsequent work
on the fast computation of mean-variance frontiers (Markowitz
(1956) and Appendix A of Markowitz (1959)). My 1959 book was
principally written at the Cowles Foundation at Yale during the
academic year 1955-56, on leave from the RAND Corporation, at the
invitation of James Tobin. It is
not clear that Markowitz (1959) would ever have been written if
it were not for Tobin's invitation.

My article on "Portfolio Selection" appeared in 1952. In the 38
years since then, I have worked with many people on many topics.
The focus has always been on the application of mathematical or
computer techniques to practical problems, particularly problems
of business decisions under uncertainty. Sometimes we applied
existing techniques; other times we developed new techniques.
Some of these techniques have been more "successful" than others,
success being measured here by acceptance in practice.

In 1989, I was awarded the Von Neumann Prize in Operations
Research Theory by the Operations Research Society of America and The Institute of Management Sciences. They cited my
works in the areas of portfolio theory, sparse matrix techniques
and the SIMSCRIPT programming language. I have written above
about portfolio theory. My work on sparse matrix techniques was
an outgrowth of work I did in collaboration with Alan S. Manne,
Tibor Fabian, Thomas Marschak, Alan J. Rowe and others at the
RAND Corporation in the 1950s on industry-wide and multi-industry
activity analysis models of industrial capabilities. Our models
strained the computer capabilities of the day. I observed that
most of the coefficients in our matrices were zero; *i.e.* ,
the nonzeros were "sparse" in the matrix, and that typically the
triangular matrices associated with the forward and back solution
provided by Gaussian elimination would remain sparse if pivot
elements were chosen with care. William Orchard-Hayes programmed
the first sparse matrix code. Since then considerable work has
been done on sparse matrix techniques, for example, on methods of
selecting pivots and of storing the nonzero elements. Sparse
matrix techniques are now standard in large linear programming
codes.

During the 1950s I decided, as did many others, that many
practical problems were beyond analytic solution, and that
simulation techniques were required. At RAND I participated in
the building of large logistics simulation models; at General
Electric I helped build models of manufacturing plants. One
problem with the use of simulation was the length of time
required to program a detailed simulator. In the early 1960s, I
returned to RAND for the purpose of developing a programming
language, later called SIMSCRIPT, which reduced programming time
by allowing the programmer to describe (in a certain stylized
manner) the system to be simulated rather than describing the
actions which the computer must take to accomplish this
simulation. The original SIMSCRIPT compiler was written by B.
Hausner; its manual by H. Karr who later co-founded a computer
software company, CACI, with me. Currently SIMSCRIPT II.5 is
supported by CACI and still has a fair number of users.

I am sorry I cannot acknowledge all the people I have worked with
over the last 38 years and describe what it was we accomplished.
As each of these people know, I often considered work to be play,
and derived great joy from our collaboration.

From *Les Prix Nobel. The Nobel Prizes 1990*, Editor Tore Frängsmyr, [Nobel Foundation], Stockholm, 1991

This autobiography/biography was written
at the time of the award and later published in the book series *Les
Prix Nobel/ Nobel Lectures/The Nobel Prizes*. The information is sometimes updated with an addendum submitted
by the Laureate.

Copyright © The Nobel Foundation 1990

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