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...

Measuring the performance of stock portfolios that include options is challenging due to options' nonlinearity in the underlying, their exposure to volatility risk, and their time decay. Our contribution to the literature is twofold: First, we provide a theoretically rigorous derivation of the...

I develop a portfolio choice model that allows for partial default and accommodates trade in a rich set of assets. I characterize the solution to an infinite horizon, consumption/portfolio problem with Markov shocks and many assets. The characterization facilitates a simple solution algorithm...

The impact of transaction costs on asset pricing in equilibrium is rarely studied. We study an equilibrium model with proportional transaction costs where two investors trade in a derivative to hedge non-traded endowments. For any positive transaction cost there always exist no trade equilibria....

We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is...

In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Amongst the numerous problems addressed, the optimal execution of large orders is probably the one that has attracted the most research works, mainly in the case of single-asset...

We investigate risk averse agents who manage risk by trading financial securities in a market that we call a risk market. We assume this market is perfectly competitive and complete. When risk aversion is expressed using risk measures, the (bundle of) prices for financial securities turns out to...

Growth Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz's mean-variance or risk parity. The GOP literature typically considers risk-neutral...

Growth Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. How it is also known in practice GOP is too risky. We explain in this talk that the reason is in practice the investment horizon is finite and practitioners account for risk more explicitly. We...

We propose a simplified approach to mean-variance portfolio problems by changing their parametrisation from trading strategies to final positions. This allows us to treat, under a very mild no-arbitrage-type assumption, a whole range of quadratic optimisation problems by simple mathematical...