Abstract
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 modeling, this approach is based on random dynamical systems. An equilibrium holds only in the short term, which reflects the model of investment behavior 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 generalization 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.
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