Optimal investment, retirement, and life insurance with consumption ratcheting and time-inhomogeneous utility
作者机构：School of Big Data Application and Economics Guizhou University of Finance and Economics School of Mathematics Southwestern University of Finance and Economics
出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))
年 卷 期：2025年
核心收录：
学科分类：12[管理学] 02[经济学] 0202[经济学-应用经济学] 1204[管理学-公共管理] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 020204[经济学-金融学（含∶保险学）] 07[理学] 070105[理学-运筹学与控制论] 120404[管理学-社会保障] 0701[理学-数学]
基 金：supported by National Natural Science Foundation of China (Grant No. 12101151) Innovation and Academic Emerging Program of Guizhou University of Finance and Economics (Grant No. 2022XSXMA19) supported by National Natural Science Foundation of China (Grant No. 12071373)
摘 要：In this paper, we study a portfolio selection problem of an investor with a retirement option, who has possibility to buy life insurance and does not tolerate any decline in consumption. The agent s optimization problem can be viewed as a mixed singular control and optimal stopping problem with time-inhomogeneous utility functions. The closed-form optimal solution is not available in general. We use the dual control method to convert the original problem into two classes of optimal stopping problems in finite and infinite *** show that the optimal consumption strategy and the best retirement time depend on the free-boundary functions which satisfy Fredholm and Volterra integral equations. We derive the closed-form formulas for these two free boundaries for some special cases and develop numerical methods to solve the integral equations of the free boundaries for general cases.
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