论文标题
关于凯利博彩中的反馈控制：一种近似方法
On Feedback Control in Kelly Betting: An Approximation Approach
论文作者
论文摘要
在本文中，我们使用著名的凯利标准考虑了一个简单的离散时间最佳博彩问题，该标准要求最大化预期的财富对数增长。虽然可以通过标准凹面编程技术解决经典的凯利投注问题，但一种替代但有吸引力的方法是调用基于泰勒的近似值，该近似将问题重新提交到二次编程中，并获得封闭形式的近似解决方案。本文的重点是在使用这种近似解决方案时提供一些有趣的属性，以填补现有结果中的一些空隙。具体而言，提供了最佳可实现的投注绩效，预期的累积增益或损失的积极性及其相关的方差，预期的增长特性，对数增长的差异以及与所谓的生存能力（无破产）有关的结果。
In this paper, we consider a simple discrete-time optimal betting problem using the celebrated Kelly criterion, which calls for maximization of the expected logarithmic growth of wealth. While the classical Kelly betting problem can be solved via standard concave programming technique, an alternative but attractive approach is to invoke a Taylor-based approximation, which recasts the problem into quadratic programming and obtain the closed-form approximate solution. The focal point of this paper is to fill some voids in the existing results by providing some interesting properties when such an approximate solution is used. Specifically, the best achievable betting performance, positivity of expected cumulative gain or loss and its associated variance, expected growth property, variance of logarithmic growth, and results related to the so-called survivability (no bankruptcy) are provided.
