MATHEMATICAL BEHAVIORAL FINANCE

Conventional models of dynamic equilibrium in asset markets are based on the principles of General Equilibrium theory (Walras, Arrow, Debreu, Radner and others). This theory in its classical form assumes that market participants are fully rational and their goals can be described in terms of the maximization of utilities subject to budget constraints. The objective of this work is to develop an alternative modelling approach admitting that market participants may have a whole variety of other patterns of behavior determined by their individual psychology, not necessarily reducible to fully rational utility maximization. The models developed do not rely upon restrictive hypotheses (perfect foresight) and avoid using unobservable agents’ characteristics such as individual utilities and beliefs, which makes them amenable to quantitative practical applications. The results obtained are concerned with fundamental questions and problems in Financial Economics such as equilibrium asset pricing and portfolio selection. The modelling frameworks combine stochastic dynamic games and evolutionary game theory. The methods employed are based on the stochastic stability analysis of nonlinear random dynamical systems.
Joint work with Rabah Amir, Economics Department, University of Iowa Thorsten Hens, Department of Banking and Finance, University of Zurich Klaus R. Schenk-Hoppé, School of Mathematics and Business School, University of Leeds