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 paper provides a novel five-component decomposition of optimal dynamic portfolio choice. It reveals the simultaneous impacts from market incompleteness and wealth-dependent utilities. The decomposition leads to implementation via either closed-form solutions or Monte Carlo simulations. With...

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 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...

The paper examines a game-theoretic evolutionary model of an asset market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The investors use general, adaptive strategies (portfolio rules), distributing their wealth between...

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...

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....

The paper examines a game-theoretic evolutionary model of a financial market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The traders use general, adaptive strategies (portfolio rules), distributing their wealth between...

Using properties of the cdf of a random variable defined as a saddle-type point of a real valued continuous stochastic process, we derive first-order asymptotic properties of tests for stochastic spanning w.r.t. a stochastic dominance relation. First, we define the concept of Markowitz...

We consider a stochastic model of a financial market with one-period assets and endogenous asset prices. The model was initially developed and analyzed in the context of Evolutionary Finance with the main focus on questions of "survival and extinction" of investment strategies (portfolio rules)....