3-Milestones Page 76 Wednesday, February 4, 2004 12:47 PM
76 The Mathematics of Financial Modeling and Investment Managementand Jan Mossin developed a theoretical model of market prices based
on the principles of financial decision-making laid down by Markowitz.
The notion of efficient markets was introduced by Paul Samuelson in
1965, and five years later, further developed by Eugene Fama.
The second round of innovation started at the end of the 1970s. In
1973, Fischer Black, Myron Scholes, and Robert Merton discovered how to
determine option prices using continuous hedging. Three years later,
Stephen Ross introduced arbitrage pricing theory (APT). Both were major
developments that were to result in a comprehensive mathematical method-
ology for investment management and the valuation of derivative financial
products. At about the same time, Merton introduced a continuous-time
intertemporal, dynamic optimization model of asset allocation. Major
refinements in the methodology of mathematical optimization and new
econometric tools were to change the way investments are managed.
More recently, the diffusion of electronic transactions has made
available a huge amount of empirical data. The availability of this data
created the hope that economics could be given a more solid scientific
grounding. A new field—econophysics—opened with the expectation
that the proven methods of the physical sciences and the newly born sci-
ence of complex systems could be applied with benefit to economics. It
was hypothesized that economic systems could be studied as physical
systems with only minimal a priori economic assumptions. Classical
econometrics is based on a similar approach; but while the scope of
classical econometrics is limited to dynamic models of time series,
econophysics uses all the tools of statistical physics and complex sys-
tems analysis, including the theory of interacting multiagent systems.THE PRECURSORS: PARETO, WALRAS, AND THE
LAUSANNE SCHOOLThe idea of formulating quantitative laws of economic behavior in ways
similar to the physical sciences started in earnest at the end of the nineteenth
century. Though quite accurate economic accounting on a large scale dates
back to Assyro-Babylonian times, a scientific approach to economics is a
recent endeavor.
Leon Walras and Wilfredo Pareto, founders of the so-called Lausanne
School at the University of Lausanne in Switzerland, were among the first
to explicitly formulate quantitative principles of market economies, stating
the principle of economic equilibrium as a mathematical theory. Both
worked at a time of great social and economic change. In Pareto’s work in
particular, pure economics and political science occupy a central place.