标题： 收入与闲暇对指数效用下最优投资组合、消费和退休决策的影响 显示英文标题

标题： Impact Of Income And Leisure On Optimal Portfolio, Consumption, Retirement Decisions Under Exponential Utility

摘要： 我们研究了一个最优控制问题，该问题涵盖了在指数（CARA型）效用下的投资、消费和退休决策。 金融市场包括一个具有常数漂移的债券和一个遵循几何布朗运动的股票。 代理人获得持续收入，随时间消费，并且有不可逆的退休选择，在退休后相比退休前获得更高的闲暇。 目标是在无限期限内最大化加权消费和闲暇的期望指数效用。 使用鞅方法和对偶值函数，我们推导了最优投资组合、消费和退休时间的隐式解。 分析突出了主要贡献：首先，无退休的等价条件由特定的收入阈值表征；其次，收入和闲暇水平对最优投资组合、消费和退休决策的影响得到了全面考察。 这些结果为退休规划中金融与生活方式选择之间的相互作用提供了有价值的见解。 显示英文摘要

摘要： We study an optimal control problem encompassing investment, consumption, and retirement decisions under exponential (CARA-type) utility. The financial market comprises a bond with constant drift and a stock following geometric Brownian motion. The agent receives continuous income, consumes over time, and has the option to retire irreversibly, gaining increased leisure post-retirement compared to pre-retirement. The objective is to maximize the expected exponential utility of weighted consumption and leisure over an infinite horizon. Using a martingale approach and dual value function, we derive implicit solutions for the optimal portfolio, consumption, and retirement time. The analysis highlights key contributions: first, the equivalent condition for no retirement is characterized by a specific income threshold; second, the influence of income and leisure levels on optimal portfolio, consumption, and retirement decisions is thoroughly examined. These results provide valuable insights into the interplay between financial and lifestyle choices in retirement planning.