Extending the Kelly Criterion: Optimizing Multi-Investment Portfolios with Bankruptcy Risks and Real-World Return Distributions

Abstract

Kelly Criteria is a well-known method for improving capital allocation to enhance long-term wealth development. Usually supposing binary conclusions and idealized return distributions, this criterion does not completely reflect the complexity of real-world financial markets, especially in circumstances of numerous investments having various bankruptcy risks. Driven by the belief that "there is no absolute truth in science; all theorems known to mankind are simply the best summaries of nature based on current knowledge and conditions," this study proposes an extension to the Kelly Criteria, considering more realistic scenarios. By explicitly incorporating the possibility of Bankruptcy for every investment and including a bimodal distribution of returns, this work aims to present a more reasonable and effective portfolio optimization approach. Designed to maximize the expected logarithmic rise of wealth and control the inherent bankruptcy risks, the extended model offers a stronger solution for investors in today's complex financial environment. This study shows that changing the Kelly Criterion to fit these real-world conditions will produce more accurate and optimal investing plans.