We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. A practical scheme for the...

The Kelly Capital Growth Investment Strategy (KCGIS) is to maximize the expected utility of nal wealth with a logarithmic utility function. This approach dates to Bernoulli's 1738 suggestion of log as the utility function arguing that marginal utility was proportional to the reciprocal of...

Leverage entails a unique set of risks, such as margin calls, which can force investors to liquidate securities at adverse prices. Investors often seek to mitigate these risks by using a leverage constraint in conventional mean-variance portfolio optimization. Mean-variance optimization,...

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...

We develop a novel Mean-Max Drawdown portfolio optimization approach using buy-and-hold portfolios. The optimization is performed utilizing a multi-objective evolutionary algorithm on a sample of S&P 100 constituents. Our optimization procedure provides portfolios with better Mean-Max Drawdown...