Adaptive strategies in Kelly's horse races model

We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. We characterize the cost of this gambling strategy and we analyze the asymptotic scaling of the difference between the growth rate of the gambler and the optimal growth rate, known as the gambler's regret. We also explain how this adaptive strategy relates to the universal portfolio strategy, and we build improved adaptive strategies in which the gambler exploits the information contained in the bookmaker odds distribution.

Automated summary

This paper presents an adaptive version of Kelly's horse model, where the gambler learns from past race results using Bayesian inference. The cost of this gambling strategy is characterized, and the difference between the growth rate of the gambler and the optimal growth rate, known as the gambler's regret, is analyzed in terms of asymptotic scaling. The study also explores the relationship between this adaptive strategy and the universal portfolio strategy, and proposes improved adaptive strategies that exploit the information contained in the bookmaker odds distribution.