In the Kelly game (Kelly,  1956 ), a gambler is allowed to invest a part of the wealth in each turn. With a certain probability this investment is doubled, and otherwise it is lost. Motivated by the complexity of real investments, we propose several modifications of this game  to investigate the influence of diversification and limited information on investment performance. Analytical and numerical results obtained from these toy games are well related to their real-life counterparts .
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 .
R
In the Kelly game (Kelly,
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
A
Kelly (
R
), a gambler is allowed to invest a part of the wealth in each turn. With a certain probability this investment is doubled, and otherwise it is lost. Motivated by the complexity of real investments, we propose several modifications of this game
)
A
that incorporates these features, and use them
R
investment performance. Analytical and numerical results obtained from these toy games are well related to their real-life counterparts
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