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This chapter surveys current research and applications of evolutionary finance inspired by Darwinian ideas and random dynamical systems theory. This approach studies the market interaction of investment strategies, and the wealth dynamics it entails in financial markets. The emphasis in this survey was on the motivation and the heuristic justification of the results; technical details were avoided as much as possible. In contrast to the current standard paradigm in economic modelling, this approach is based on random dynamical systems. An equilibrium holds only in the short term, which reflects the model of investment behaviour explored in an evolutionary finance approach. Continuous-time evolutionary finance models are the latest development in this field. This approach can be seen as a generalisation of the workhorse model of continuous-time financial mathematics. One advantage of this model is the flexibility to have different trade frequencies and changes in dividend payments.
Evolutionary finance studies the dynamic interaction of investment strategies in financial markets. This market interaction generates a stochastic wealth dynamic on a heterogenous population of traders through the fluctuation of asset prices and their random payoffs. Asset prices are endogenously determined through short-term market clearing. Investors' portfolio choices are characterized by investment strategies that provide a descriptive model of decision behavior. The mathematical framework of these models is given by random dynamical systems.
This chapter surveys the recent progress made by the authors in the theory and applications of evolutionary finance models. An introduction to and the motivation of the modeling approach is followed by a theoretical part that presents results on the market selection (and coexistence) of investment strategies, discusses the relation to the Kelly Rule and implications for asset-pricing theory, and introduces a continuous-time mathematical finance version. Applications are concerned with simulation studies of market dynamics, empirical estimation of asset prices and their dynamics, and evolution of investment strategies using genetic programming.",
Genetic Programming entries for Igor V Evstigneev Thorsten Hens Klaus Reiner Schenk-Hoppe