英文标题：
《Risk-Constrained Kelly Gambling》
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作者：
Enzo Busseti, Ernest K. Ryu, Stephen Boyd
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最新提交年份：
2016
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英文摘要：
We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown probability; using this bound instead of the original risk constraint yields a convex optimization problem that guarantees the drawdown risk constraint holds. Numerical experiments show that our bound on drawdown probability is reasonably close to the actual drawdown risk, as computed by Monte Carlo simulation. Our method is parametrized by a single parameter that has a natural interpretation as a risk-aversion parameter, allowing us to systematically trade off asymptotic growth rate and drawdown risk. Simulations show that this method yields bets that out perform fractional-Kelly bets for the same drawdown risk level or growth rate. Finally, we show that a natural quadratic approximation of our convex problem is closely connected to the classical mean-variance Markowitz portfolio selection problem.
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中文摘要：
我们考虑了具有一般结果分布的经典凯利赌博问题，以及一个额外的风险约束，该约束将财富减少的概率限制在给定的不良水平。我们给出了下降概率的一个界；使用这个界限而不是原始的风险约束会产生一个凸优化问题，该问题保证了提取风险约束成立。数值实验表明，根据蒙特卡罗模拟计算，我们的水位下降概率界限与实际水位下降风险相当接近。我们的方法由一个单独的参数进行参数化，该参数具有风险规避参数的自然解释，允许我们系统地权衡渐进增长率和下降风险。仿真结果表明，在相同的提款风险水平或增长率下，该方法产生的赌注超过了分数凯利赌注。最后，我们证明了凸问题的一个自然二次逼近与经典的均值-方差Markowitz投资组合问题密切相关。
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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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