A Continuous Time Approximation of an Evolutionary Stock Market Model

Abstract

We derive a continuous time approximation of the evolutionary market selection model of Blume & Easley (1992). Conditions on the payoff structure of the assets are identified that guarantee convergence. We show that the continuous time approximation equals the solution of an integral equation in a random environment. For constant asset returns, the integral equation reduces to an autonomous ordinary differential equation. We analyze its long-run asymptotic behavior using techniques related to Lyapunov functions, and compare our results to the benchmark of profit-maximizing investors.

Keywords: Portfolio theory, evolutionary finance, incomplete markets, continuous time Euler approximation, stochastic processes in random environments, integral equation, ordinary differential equation, Lyapunov function

JEL Classification: D52, D81, D83, G11