Numerical Simulation of a Diffusion Type Evolutionary Stock Market Model
19 Pages Posted: 26 Feb 2008
Date Written: February 22, 2008
We adapt the evolutionary stock market model from Evstigneev, Hens, Schenk-Hoppé (2006) to a continuous time framework, where uncertainty in dividends is produced by a single Wiener process. The setup is therefore significantly different from Yang and Ewald (2008), who also study continuous time, but remain within the framework of random dynamical systems of non-diffusive type. For the case of fix-mix strategies we derive the stochastic differential equation which determines the evolution of the wealth processes of the various market players. These stochastic differential equations are highly non-linear and we find that it is impossible to solve them analytically. Instead we simulate the wealth dynamic for various initial setups of the market. A detailed discussion of our observations from the simulations is given.
Keywords: Behavioral Finance, Evolutionary Finance, Wealth dynamics
JEL Classification: C63, G11, G31, G39
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