英文标题：
《Robust Markowitz mean-variance portfolio selection under ambiguous
covariance matrix *》
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作者：
Amine Ismail (LPMA), Huy\\^en Pham (LPMA, CREST)
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最新提交年份：
2017
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英文摘要：
This paper studies a robust continuous-time Markowitz portfolio selection pro\\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman-Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies and illustrate our results in the case of uncertain volatilities and ambiguous correlation between two risky assets. We then derive the robust efficient frontier in closed-form, and obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy. Finally, we compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model. MSC Classification: 91G10, 91G80, 60H30
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中文摘要：
本文研究了一个稳健的连续时间马科维茨投资组合选择问题，其中模型的不确定性包含多个风险资产的协方差矩阵。该问题被表述为一组非占优概率测度上的最小-最大均值-方差问题，该问题由McKean-Vlasov动态规划方法解决，该方法允许我们根据Wasserstein概率测度空间中的Bellman-Isaacs方程来描述解。我们为最优稳健投资组合策略提供了明确的解决方案，并在波动率不确定和两种风险资产之间的相关性不明确的情况下说明了我们的结果。然后，我们导出了封闭形式的鲁棒有效前沿，并获得了任何鲁棒有效投资组合策略的夏普比的下界。最后，我们比较了稳健投资者和错误模型投资者的夏普比率表现。MSC分类：91G10、91G80、60H30
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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：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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