Learning strategies in Kelly's horse model

We define Kelly's strategy for the horse race model, describing the concept of growth rate. We outline an adaptive strategy from Despons et al., in which the gambler uses Bayesian inference to try and learn the win probabilities of the horses. We implement a modified version of this strategy, using our knowledge of the payoffs. Moreover, we use a Bayesian model selection approach to the problem, in the framework of Haimovici et al. Lastly, we go back to the modified Bayesian inference approach and devise a strategy that aims to maximize a linear combination of the expected value and the variance of the growth rate.