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Optimal Consumption and Investment with Independent Stochastic Labor Income

Author

Listed:
  • Alain Bensoussan

    (Jindal School of Management, University of Texas at Dallas, Austin, Texas 78712; and School of Data Science, City University Hong Kong, Kowloon Tong, Hong Kong)

  • Seyoung Park

    (Nottingham University Business School, University of Nottingham University Park, Nottingham NG7 2RD)

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.

Suggested Citation

  • Alain Bensoussan & Seyoung Park, 2025. "Optimal Consumption and Investment with Independent Stochastic Labor Income," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 356-389, February.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:1:p:356-389
    DOI: 10.1287/moor.2023.0119
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