Adaptive strategy in Kelly's horse races model

TL;DR

This paper develops an adaptive betting strategy based on Bayesian inference in Kelly's horse race model, improving capital growth by exploiting bookmaker odds and connecting to universal portfolio strategies.

Contribution

It introduces an adaptive Bayesian approach to Kelly's model, linking it to universal portfolios and enhancing initial capital preservation during learning.

Findings

Recovered known asymptotic gambler's regret scaling.

Established relation between adaptive strategy and universal portfolio.

Designed improved strategies exploiting bookmaker odds for better performance.

Abstract

We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. A known asymptotic scaling for the difference between the growth rate of the gambler and the optimal growth rate, known as the gambler'sregret, is recovered. We show how this adaptive strategy is related to the universal portfolio strategy, and we build improved adaptive strategies in which the gambler exploits information contained in the bookmaker odds distribution to reduce his/her initial loss of the capital during the learning phase.