Faculté des sciences

Diversification and limited information in the Kelly game

Medo, Matúš ; Pis’mak, Yury M. ; Zhang, Yi-Cheng

In: Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, no. 24, p. 6151-6158

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 [J.L. Kelly, IEEE Transactions on Information Theory 2 (1956) 185–189] that incorporates these features, and use them to investigate... Plus

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    Summary
    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 [J.L. Kelly, IEEE Transactions on Information Theory 2 (1956) 185–189] 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.