英文标题：
《Kelly Betting Can Be Too Conservative》
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作者：
Chung-Han Hsieh, B. Ross Barmish, and John A. Gubner
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最新提交年份：
2017
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英文摘要：
  Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes arguments that the theory often leads to bets which are \"too aggressive\" with respect to various risk metrics. To remedy this problem, many papers include prescriptions for scaling down the bet size. Such schemes are referred to as Fractional Kelly Betting. In this paper, we take the opposite tack. That is, we show that in many cases, the theoretical Kelly-based results may lead to bets which are \"too conservative\" rather than too aggressive. To make this argument, we consider a random vector X with its assumed probability distribution and draw m samples to obtain an empirically-derived counterpart Xhat. Subsequently, we derive and compare the resulting Kelly bets for both X and Xhat with consideration of sample size m as part of the analysis. This leads to identification of many cases which have the following salient feature: The resulting bet size using the true theoretical distribution for X is much smaller than that for Xhat. If instead the bet is based on empirical data, \"golden\" opportunities are identified which are essentially rejected when the purely theoretical model is used. To formalize these ideas, we provide a result which we call the Restricted Betting Theorem. An extreme case of the theorem is obtained when X has unbounded support. In this situation, using X, the Kelly theory can lead to no betting at all.
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中文摘要：
凯利赌博是一种在一组赌博中进行最优资源分配的处方，这些赌博通常以独立且相同的分布方式重复。在这种情况下，有大量文献包括这样的论点，即该理论通常会导致在各种风险度量方面“过于激进”的下注。为了解决这个问题，许多论文都提供了缩小赌注规模的处方。这种方案被称为分数凯利下注。在本文中，我们采取相反的策略。也就是说，我们表明，在许多情况下，基于凯利的理论结果可能会导致“过于保守”而不是过于激进的下注。为了证明这一点，我们考虑一个随机向量X及其假设的概率分布，并抽取m个样本以获得一个经验推导的对应Xhat。随后，我们推导并比较了X和Xhat的Kelly下注结果，并将样本量m作为分析的一部分。这导致识别出许多具有以下显著特征的情况：使用X的真实理论分布得到的下注大小比Xhat的小得多。相反，如果赌注是基于经验数据，则会发现“黄金”机会，而当使用纯理论模型时，这些机会基本上被拒绝。为了将这些想法形式化，我们提供了一个结果，我们称之为受限下注定理。当X有无界支撑时，得到了该定理的一个极端情况。在这种情况下，使用X，凯利理论可能导致根本没有下注。
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分类信息：

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
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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
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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