英文标题：
《Optimal investment with time-varying stochastic endowments》
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作者：
Christoph Belak, An Chen, Carla Mereu, Robert Stelzer
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最新提交年份：
2021
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英文摘要：
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the value function for general utility functions, we rely on the dynamic programming approach to solve the optimization problem for power utility investors including the empirically relevant and mathematically challenging case of relative risk aversion larger than one. For this, we argue that the value function is the unique viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation. The homogeneity of the value function is then used to reduce the HJB equation by one dimension, which allows us to prove that the value function is even a classical solution thereof. Using this, an optimal strategy is derived and its asymptotic behavior in the large wealth regime is discussed.
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中文摘要：
本文考虑了一个效用最大化和最优资产配置问题，该问题存在一个不能通过金融市场交易完全对冲的随机捐赠。在研究了一般效用函数的值函数的连续性之后，我们利用动态规划方法来解决电力效用投资者的优化问题，包括相对风险规避大于1的经验相关且数学上具有挑战性的情况。为此，我们认为值函数是Hamilton-Jacobi-Bellman（HJB）方程的唯一粘性解。然后利用值函数的齐次性将HJB方程简化为一维，从而证明值函数甚至是其经典解。利用这一点，我们导出了一个最优策略，并讨论了它在大财富状态下的渐近行为。
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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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