论文标题
在跳跃扩散市场中的习惯持久性的退休决定
Retirement decision with addictive habit persistence in a jump diffusion market
论文作者
论文摘要
本文考虑了习惯持久性和股票工资相关性，研究了市场中最佳的退休决定，投资和消费策略。我们的分析考虑了多个股票和有限的时间框架，以确定``财富 - 贸易工资''三胞胎$（x，h，w）$的退休边界。为了实现这一目标，我们使用习惯方法和二元性方法来获得对原始变量和最佳策略的挑战的范围的保留范围，以确定diparts of Fimest tragition nequient of Decition of Dectife of Decortion。使用$ C^1 $版本的最佳退休边界$ \ hat {\ rm o} $的公式。}我们的结果表明，当所谓的``事实上的财富''超过工资的关键比例时，立即退休是代理人的最佳选择。此外，我们发现跳跃风险的引入允许在工作区域内不连续的投资策略，这是一个新颖而有见地的发现。我们的数值结果通过改变参数有效地说明了这些发现。
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.
