Optimal Consumption and Investment with Independent Stochastic Labor Income

• 成果类型: Article
• 署名作者: Bensoussan, Alain; Park, Seyoung
• 署名单位: University of Texas System; University of Texas Dallas; City University of Hong Kong; University of Nottingham
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0119
• 发表日期: 2025
• 关键词: portfolio choice; life-cycle; Early retirement; selection; DECOMPOSITION; policies; MARKETS

摘要

We develop a new dynamic continuous -time model of optimal consumption and investment to include independent stochastic labor income. We reduce the problem of solving the Bellman equation to a problem of solving an integral equation. We then explicitly characterize the optimal consumption and investment strategy as a function of incometo -wealth ratio. We provide some analytical comparative statics associated with the value function and optimal strategies. We also develop a quite general numerical algorithm for control iteration and solve the Bellman equation as a sequence of solutions to ordinary differential equations. This numerical algorithm can be readily applied to many other optimal consumption and investment problems especially with extra nondiversifiable Brownian risks, resulting in nonlinear Bellman equations. Finally, our numerical analysis illustrates how the presence of stochastic labor income affects the optimal consumption and investment strategy.