Key result
A generalization of Kelly's horse model explores the trade-off between mean growth rate and extinction probability as an alternative definition of risk for biological and ecological applications.
Why the study?
To examine a generalization of Kelly's horse model where gambling on non-winning horses does not cause complete investment loss, evaluating growth and risk.
The paper provides a theoretical generalization of Kelly's gambling model to non-diagonal odds matrices, with implications for risk-return trade-offs in biological and ecological systems.
Alternative risk metric via growth-extinction trade-off may inform ecological decisions; leaves open empirical validation in biological systems.
We study a generalization of Kelly’s horse model to situations where gambling on horses other than the winning horse does not lead to a complete loss of the investment. In such cases, the odds matrix is non-diagonal, which is particularly interesting for biological applications. We examine the trade-off between the mean growth rate and its asymptotic variance, an approximation for risk. Because the consequences of fluctuations around the average growth rate are asymmetric, we further explore a better alternative definition of risk: the extinction probability and its implications for Kelly gambling and the risk-return trade-off. We discuss some applications of these concepts in biology and ecology.
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Cavallero et al. (2024) studied this question. Generalization of Kelly's horse model was evaluated. A generalization of Kelly's horse model explores the trade-off between mean growth rate and extinction probability as an alternative definition of risk for biological and ecological applications.
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