英文标题：
《At What Frequency Should the Kelly Bettor Bet?》
---
作者：
Chung-Han Hsieh, B. Ross Barmish, John A. Gubner
---
最新提交年份：
2018
---
英文摘要：
  We study the problem of optimizing the betting frequency in a dynamic game setting using Kelly\'s celebrated expected logarithmic growth criterion as the performance metric. The game is defined by a sequence of bets with independent and identically distributed returns X(k). The bettor selects the fraction of wealth K wagered at k = 0 and waits n steps before updating the bet size. Between updates, the proceeds from the previous bets remain at risk in the spirit of \"buy and hold.\" Within this context, the main questions we consider are as follows: How does the optimal performance, we call it gn*, change with n? Does the high-frequency case, n = 1, always lead to the best performance? What are the effects of accrued interest and transaction costs? First, we provide rather complete answers to these questions for the important special case when X(k) in {-1,1} is a Bernoulli random variable with probability p that X(k) = 1. This serves as an entry point for future research using a binomial lattice model for stock trading. The latter sections focus on more general probability distributions for X(k) and two conjectures. The first conjecture is simple to state: Absent transaction costs, gn* is non-increasing in n. The second conjecture involves the technical condition which we call the sufficient attractiveness inequality. We first prove that satisfaction of this inequality is sufficient to guarantee that the low-frequency bettor using large n can match the performance of the high-frequency bettor using n = 1. Subsequently, we conjecture, and provide supporting evidence that this condition is also necessary.
---
中文摘要：
我们使用Kelly著名的期望对数增长准则作为性能度量，研究了动态博弈环境中的下注频率优化问题。游戏由一系列具有独立且相同分布回报X（k）的下注定义。下注者选择K=0时下注的财富K的分数，并等待n步，然后更新下注大小。在两次更新之间，基于“买入并持有”的精神，先前赌注的收益仍处于风险之中在此背景下，我们考虑的主要问题如下：最佳性能（我们称之为gn*）如何随n变化？高频情况下，n=1，是否总是导致最佳性能？应计利息和交易成本的影响是什么？首先，对于{1,1}中的X（k）是概率p为X（k）=1的伯努利随机变量的重要特例，我们提供了这些问题的相当完整的答案。这是未来使用二项式晶格模型进行股票交易研究的切入点。后几节重点讨论X（k）的更一般的概率分布和两个猜想。第一个猜想很容易说明：在没有交易成本的情况下，gn*在n中不增加。第二个猜想涉及技术条件，我们称之为充分吸引不等式。我们首先证明了满足这个不等式足以保证使用大n的低频投注器可以与使用n=1的高频投注器的性能相匹配。随后，我们猜测，并提供支持证据，证明该条件也是必要的。
---
分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
--
一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--
一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--
一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
--

---
PDF下载：
-->