BFS 2002

Plenary Address

Probabilistic Aspects of Portfolio Analysis and Optimization

Ioannis Karatzas, Robert Fernholz

We discuss the concept of "diversity" for a financial market, which means roughly that no single asset is allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated by Samuelson, we formulate this property in precise terms and show that diversity is indeed possible, though rather delicate, to achieve. We provide examples demonstrating that diverse financial markets contain arbitrage opportunities, over sufficiently long time-horizons.