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 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...

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 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...

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...

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 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)....

Evolutionary Finance (EF) explores financial markets as evolving biological systems. Investors pursuing diverse investment strategies compete for the market capital. Some "survive" and some "become extinct". A central goal is to identify evolutionary stable (in one sense or another) investment...