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 was observed, and superior returns were achieved taking it into consideration.

中文翻译：

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凯利（Kelly）投注不确定性的赛马

我们调查结果概率不确定的赌博问题。当使用多项逻辑回归估计概率时，建议使用随机优化模型对具有互斥结果的事件进行最佳投资。特别注意有两个结果的情况和许多结果的一般情况。进行了使用模拟数据的实证研究，观察到了概率估计误差带来的回报损失，并考虑了这一点而获得了较高的回报。