Diversification and limited information in the Kelly game

TL;DR

This paper explores how diversification and limited information affect Kelly-optimal investment strategies, providing formulas and results for optimizing portfolios under these realistic market conditions.

Contribution

It introduces generalized Kelly game models incorporating diversification and limited information, offering new formulas and exact solutions for portfolio optimization.

Findings

Approximate formulas for diversified portfolio optimization

Exact results for investment with limited information

Insights into the impact of diversification and information constraints

Abstract

Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game [Kelly (1956)] that incorporates these features, and use them to investigate the influence of diversification and limited information on Kelly-optimal portfolios. In particular we present approximate formulas for optimizing diversified portfolios and exact results for optimal investment in unknown games where the only available information is past outcomes.