跳跃扩散市场中具有成瘾性习惯持久性的退休决策
Retirement decision with addictive habit persistence in a jump diffusion market
AI总结：
本文研究跳跃扩散市场中考虑习惯持久性和股票-工资相关性的最优退休、投资与消费策略，通过习惯降维与对偶方法确定退休边界，发现事实财富超临界值时立即退休最优，且跳跃风险导致工作区投资策略可能不连续。
摘要：
本文研究了在跳跃扩散市场中考虑习惯持久性和股票-工资相关性的最优退休决策、投资和消费策略。我们的分析考虑了多只股票和有限时间框架，旨在确定“财富-习惯-工资”三元组 $(x, h, w)$ 的退休边界。为此，我们使用习惯降维方法和对偶方法，获得了原始变量的退休边界和最优策略的反馈形式。在处理对偶问题时，我们使用 Itô 公式的 $C^1$ 版本，解决了最优退休边界积分方程特征化证明中的技术挑战。结果表明，当所谓的“事实财富”超过工资的临界比例时，立即退休是智能体的最优选择。此外，我们发现跳跃风险的引入使得工作区域内可能出现不连续的投资策略，这是一个新颖且有见地的发现。数值结果通过改变参数有效说明了这些发现。
英文摘要：
This paper investigates the optimal retirement decision, investment, and consumption strategies in a market with jump diffusion, taking into account habit persistence and stock-wage correlation. Our analysis considers multiple stocks and a finite time framework, intending to determine the retirement boundary of the ``wealth-habit-wage" triplet $(x, h, w)$. To achieve this, we use the habit reduction method and a duality approach to obtain the retirement boundary of the primal variables and feedback forms of optimal strategies. { When dealing with the dual problem, we address technical challenges in the proof of integral equation characterization of optimal retirement boundary using a $C^1$ version of It$\hat{\rm o}$'s formula.} Our results show that when the so-called ``de facto wealth" exceeds a critical proportion of wage, an immediate retirement is the optimal choice for the agent. Additionally, we find that the introduction of jump risks allows for the possibility of discontinuous investment strategies within the working region, which is a novel and insightful finding. Our numerical results effectively illustrate these findings by varying the parameters.
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