This chapter gives an overview of current research in evolutionary finance. We mainly focus on the survival and stability properties of investment strategies associated with the Kelly rule. Our approach to the study of the wealth dynamics of investment strategies is inspired by Darwinian ideas...

This chapter surveys theoretical research on the long-term performance of fixed-mix investment strategies. These self-financing strategies rebalance the portfolio over time so as to keep constant the proportions of wealth invested in various assets. The main result is that wealth can be grown...

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev, Pirogov and...

This paper studies the wealth dynamics of investors holding self-financing portfolios in a continuous-time model of a financial market. Asset prices are endogenously determined by market clearing. We derive results on the asymptotic dynamics of the wealth distribution and asset prices for...

The paper examines a game-theoretic model of a financial market in which asset prices are determined endogenously in terms of a short-run equilibrium. Investors use general, adaptive strategies (portfolio rules) depending on the exogenous states of the world and the observed history of the game....

Evolutionary finance studies the dynamic interaction of investment strategies in financial markets. This market interaction generates a stochastic wealth dynamics on a heterogenous population of traders through the fluctuation of asset prices and their random payoffs. Asset prices are...

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...

This paper complements theoretical studies on the Kelly rule in evolutionary finance by studying a Darwinian model of selection and reproduction in which the diversity of investment strategies is maintained through genetic programming. We find that investment strategies which optimize long-term...

We introduce an evolutionary equilibrium asset pricing model with heterogeneous agents who can either act as brokers or hedge funds. Hedge funds can trade on margin, taking short or (leveraged) long positions in the assets. Brokers provide asset loans and credit to margin traders. In any...

We quantify the effects of financial regulation in a general equilibrium model with market microstructure. Fund managers trade stocks and bonds in an order-driven market, subject to transaction taxes and constraints on short-selling and leverage. Results are obtained on the equilibrium...