3-Milestones Page 75 Wednesday, February 4, 2004 12:47 PM

CHAPTER

3

Milestones in Financial Modeling

and Investment Management

T

he mathematical development of present-day economic and finance

theory began in Lausanne, Switzerland at the end of the nineteenth

century, with the development of the mathematical equilibrium theory by

Leon Walras and Wilfredo Pareto.^1 Shortly thereafter, at the beginning of

the twentieth century, Louis Bachelier in Paris and Filip Lundberg in Upp-

sala (Sweden) made two seminal contributions: they developed sophisti-

cated mathematical tools to describe uncertain price and risk processes.

These developments were well in advance of their time. Further

progress was to be made only much later in the twentieth century, thanks

to the development of digital computers. By making it possible to com-

pute approximate solutions to complex problems, digital computers

enabled the large-scale application of mathematics to business problems.

A first round of innovation occurred in the 1950s and 1960s. Ken-

neth Arrow and Georges Debreu introduced a probabilistic model of

markets and the notion of contingent claims. (We discuss their contribu-

tions in Chapter 6.) In 1952, Harry Markowitz described mathemati-

cally the principles of the investment process in terms of utility

optimization. In 1961, Franco Modigliani and Merton Miller clarified

the nature of economic value, working out the implications of absence

of arbitrage. Between 1964 and 1966, William Sharpe, John Lintner,

(^1) References for some of the works cited in this chapter will be provided in later chap-
ters in this book. For an engaging description of the history of capital markets see
Peter L. Bernstein, Capital Ideas (New York: The Free Press, 1992). For a history of
the role of risk in business and investment management, see Peter L. Bernstein,
Against the Gods (New York: John Wiley & Sons, 1996).
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