The limit distribution of evolving strategies in financial markets

This paper reconsiders the popular Brock and Hommes [Brock, W. A., and C. H. Hommes. 1997. "A Rational Route to Randomness." Econometrica 65: 1059-1096.] framework for the study of the evolution of agents' choices when different behavioural strategies are available. In particular, we model the intensity of choice as an endogenous variable and not a parameter as it is commonly treated in the literature. We make use of the maximum entropy inference to obtain an analogous exponential type probability function for strategies, with the intensity of choice varying over time according to the performance of each strategy. We test this approach on an existing asset pricing model, highlighting the effects on the system of the different switching pattern that originate in the endogenous switching intensity.