英文标题：
《Epstein-Zin Utility Maximization on a Random Horizon》
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作者：
Joshua Aurand, Yu-Jui Huang
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最新提交年份：
2021
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英文摘要：
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed-horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies.
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中文摘要：
本文在随机视界上求解了Epstein-Zin偏好下的消费投资问题。在不完全市场中，我们将随机视界视为适应市场过滤的停止时间，由所有可观察但不一定可交易的状态过程生成。与之前的研究相反，我们没有对随机视界施加任何固定的上界，允许真正的无界。针对风险厌恶和跨期替代弹性均大于1的经验相关案例，我们利用无界随机视界上具有超线性增长的倒向随机微分方程刻画了最优消费和投资策略。与经典的固定视界结果相比，这种表征涉及一个额外的随机过程，用于捕捉视界的随机性。如两个具体例子所示，从固定视界到随机视界的变化极大地改变了最优策略。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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