论文标题
最佳投注策略的相位过渡
Phase transitions in optimal strategies for betting
论文作者
论文摘要
凯利（Kelly）的标准是一种博彩策略，可最大程度地提高长期增长率，但已知风险。在这里，我们找到了最佳的投注策略，可提供最高的资本增长率，同时保持一定的风险波动价值低。然后，我们分析了在赛马模型中，平均值和增长率波动之间的权衡，首先是两匹马，然后是任意数量的马匹，以及不相关或相关的种族。我们发现了一个相变的类似物，具有两个最佳策略之间的共存，其中一个具有风险，而另一种则没有。上面的权衡也体现在平均增长率的一般情况下，类似于热力学不确定性关系。我们还在数学上证明了凯利观点和无风险策略之间没有其他相位过渡。
Kelly's criterion is a betting strategy that maximizes the long term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky fluctuations. We then analyze the trade-off between the average and the fluctuations of the growth rate, in models of horse races, first for two horses then for an arbitrary number of horses, and for uncorrelated or correlated races. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not. The above trade-off is also embodied in a general bound on the average growth rate, similar to thermodynamic uncertainty relations. We also prove mathematically the absence of other phase transitions between Kelly's point and the risk free strategy.
