La Razonable Efectividad De Las Matematicas

THE REASONABLE EFFECTIVENESS OF MATHEMATICS IN ECONOMICS
Sergio M Focardi; Frank J Fabozzi
American Economist; Spring 2010; 55, 1; ABI/INFORM Global pg. 19
THE REASONABLE EFFECTIVENESS OF MATHEMATICS
IN ECONOMICS
by Sergio M. Focardi* and Frank J. Fabozzi**

Abstract
Economic science is generally considered less viable than the physical sciences. Sophisticated mathematical models of theeconomy have been developed but their accuracy is questionable to the point that the present economic crisis is often blamed on an unwarranted faith in faulty mathematical models. In this paper, we claim that the mathematical handling of economics has actually been reasonably successful and that models are not the cause behind the present crisis. The science of economics does not study immutablelaws of nature but the complex human artifacts that are our economies and our financial markets, artifacts that are designed to be largely uncertain. We could make our economies and our markets less subject to uncertainty, and mathematical models more faithful to empirical data by introducing more rules and collecting more data. Collectively, we have decided not to do so and therefore models canonly be moderately accurate. Still, our mathematical models offer a valuable design tool to engineer our economic systems. But the mathematics of economics and finance cannot be that of physics. The mathematics of economics and finance is the mathematics of learning and com- plexity, similar to the mathematics used in studying biological or ecological systems.
Keywords: General equilibrium theories,Mathematical economics, Econometrics, Econophysics, Derivatives

1. Introducción
In 1960 the physicist Eugene Wigner, recipient of the 1962 Nobel Prize in Physics, wrote the now famous paper The Unreasonable Effectiveness of Mathematics in The Natural Sciences. Wigner (1960) argued that the success of mathematics in describing natural phenomena is so extraordinary that it is in itself aphenomenon that calls for ex- planation. In this paper, we argüe that mathematics in economics is reasonably effective and that the reasons why it is reasonably effective deserve an explanation. At the moment of this writing, the world is going through the worst financial and economic crisis since the Great Depression. Many have pointed their fingers at the growing use of mathematical models. We arguethat mathematics does not have much to do with the present crisis.
We do so first by discussing the fundamental reasons why it is possible to apply mathematics to economics and then by arguing that the use of mathematics in economics and finance can pro-duce, and indeed has produced, reasonably accu-rate forecasts. The object of science is to forecast; the mathematical models used in economics cando a reasonably good job of predicting some econom-ic events and can provide information about when it is not possible to make reliable forecasts. In addition, it is possible to outline a research agenda that would improve the science of economics. In any other science, the aforementioned would be considered a satisfactory achievement.
In a nutshell, we believe that the reason that mathematicsis only reasonably effective in eco-nomics is because we apply mathematics to study large engineered artifacts (i.e., economies or fin-ancial markets), that have been designed to allow a lot of freedom so as to encourage change and innovation. The level of unpredictability and control is clearly different when considering systems governed by immutable natural laws as opposed to artifactsconstructed by humans. Some systems, such as economies or financial markets, are prone to crises. Mathematics does a reasonably good job in describing these systems. But the mathematics involved is not that of physics: It is the mathematics of learning and complexity.
The reasonable effectiveness of mathematics in economics is important in deciding on how to prepare and train doctoral students in...