Science and social science: econophysics?

Economics and finance have for long used concepts drawn from the exact sciences. Famous economists such as Vilfredo Pareto, Nobel Prize winners Paul Samuelson and Maurice Allais, and many others, all used concepts from the exact sciences in order to aid them in modeling economic phenomena.

As we mentioned already in a footnote in Section 1.18 of Chapter 1, Louis Bachelier [1] submitted in 1900 a doctoral thesis in mathematics on the use of a Brownian motion (of the arithmetic type) as a general descriptor of an asset price process. Paul Samuelson [2] proposed, 60 years later, to use the geometric Brownian motion so as to allow for the fact that asset prices cannot be negative. This Brownian motion becomes then a major ingredient in the famous Black-Scholes option pricing theory [3].

The famous American mathematician, John von Neumann (with economist O. Morgenstern), wrote the basics of game theory. Their book [4], entitled Theory of Games and Economic Behavior, which first appeared in 1947, is the “classic” of any game theorist's library.

Important contributions to theoretical economics were also proposed by Gerard Debreu [5], a Nobel Prize winner in economics (and a mathematician by training), on the development of the so-called core of the economy.

Leonard Savage [6], a famous statistician, developed the Savage expected utility model (1954), where subjective probabilities are used in the calculation of expected utility. Robert Aumann [7], also a mathematician by training and a recent economics Nobel Prize laureate, developed the so-called Anscombe-Aumann approach (1963), where expected utility is measured with a mixture of subjective and objective probabilities.