From Discrete to Continuous Time Evolutionary Finance Models

Abstract

This paper aims to open a new avenue for research in continuous-time financial market models with endogenous prices and heterogenous investors. The main result is the derivation of the limit of a discretetime evolutionary stock market model as the length of the time period tends to zero. The resulting explicit model in continuous-time generalizes the workhorse model of mathematical finance by introducing asset prices that are driven by the market interaction of investors following self-financing trading strategies. Our approach also offers a numerical scheme for the simulation of the continuous-time model.