Optimal Consumption and Investment with Independent Stochastic Labor Income

Bensoussan, Alain; Park, Seyoung

Abstract

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 income-to-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.

Citation

Bensoussan, A., & Park, S. (2024). Optimal Consumption and Investment with Independent Stochastic Labor Income. Mathematics of Operations Research, https://doi.org/10.1287/moor.2023.0119

• Journal Article Type: Article
• Acceptance Date: Jan 22, 2024
• Online Publication Date: Mar 5, 2024
• Publication Date: Mar 5, 2024
• Deposit Date: Jan 26, 2024
• Publicly Available Date: Jan 31, 2024
• Journal: Mathematics of Operations Research
• Print ISSN: 0364-765X
• Electronic ISSN: 1526-5471
• Publisher: INFORMS
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1287/moor.2023.0119
• Keywords: optimal consumption and investment; stochastic income; Bellman equation; dynamic pro- gramming
• Public URL: https://nottingham-repository.worktribe.com/output/30150557
• Publisher URL: https://pubsonline.informs.org/doi/10.1287/moor.2023.0119