2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209946Financial 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.11 pages, 4 figuresPortfolio ManagementData Analysis, Statistics and ProbabilityPhysics and SocietyApplicationstext