英文标题：
《Continuous-Time Portfolio Choice Under Monotone Mean-Variance
Preferences-Stochastic Factor Case》
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作者：
Jakub Trybu{\\l}a and Dariusz Zawisza
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最新提交年份：
2020
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英文摘要：
We consider an incomplete market with a nontradable stochastic factor and a continuous time investment problem with an optimality criterion based on monotone mean-variance preferences. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to find an optimal investment strategy and the value function. What is more, we show that our solution is also optimal for the classical Markowitz problem and every optimal solution for the classical Markowitz problem is optimal also for the monotone mean-variance preferences. These results are interesting because the original Markowitz functional is not monotone, and it was observed that in the case of a static one-period optimization problem the solutions for those two functionals are different. In addition, we determine explicit Markowitz strategies in the square root factor models.
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中文摘要：
我们考虑了一个具有不可交易随机因素的不完全市场和一个基于单调均值-方差偏好的最优性准则的连续时间投资问题。我们将其描述为一个随机微分对策问题，并使用Hamilton-Jacobi-Bellman-Isaacs方程来寻找最优投资策略和价值函数。此外，我们还证明了我们的解对于经典Markowitz问题也是最优的，对于单调均值-方差偏好，经典Markowitz问题的每个最优解也是最优的。这些结果很有趣，因为原始的Markowitz泛函不是单调的，并且观察到在静态单周期优化问题的情况下，这两个泛函的解是不同的。此外，我们在平方根因子模型中确定了明确的马科维茨策略。
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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：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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