Kelly betting on horse races with uncertainty in probability estimates

We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using multinomial logistic regression. Special attention is given to the case of there being two outcomes, and the general case of many outcomes. An empirical study using simulated data was conducted where the loss of return from probability estimation error is observed, and superior returns are achieved taking it into consideration.