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A Risk Extended Version of Merton’s Optimal Consumption and Portfolio Selection

Author

Listed:
  • Alain Bensoussan

    (International Center for Decision and Risk Analysis, Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75083; The School of Data Science, City University of Hong Kong, 999077, Hong Kong)

  • SingRu (Celine) Hoe

    (College of Business, Texas A&M University–Commerce, Commerce, Texas 75428)

  • Joohyun Kim

    (International Center for Decision and Risk Analysis, Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75083)

  • Zhongfeng Yan

    (Department of Mathematics, Jinan University, Guangzhou, Guangdong 510632, China)

Abstract

The objective of this paper is to study the optimal consumption and portfolio choice problem of risk-controlled investors who strive to maximize total expected discounted utility of both consumption and terminal wealth. Risk is measured by the variance of terminal wealth, which introduces a nonlinear function of the expected value into the control problem. The control problem presented is no longer a standard stochastic control problem but rather, a mean field-type control problem. The optimal portfolio and consumption rules are obtained explicitly. Numerical results shed light on the importance of controlling variance risk. The optimal investment policy is nonmyopic, and consumption is not sacrificed.

Suggested Citation

  • Alain Bensoussan & SingRu (Celine) Hoe & Joohyun Kim & Zhongfeng Yan, 2022. "A Risk Extended Version of Merton’s Optimal Consumption and Portfolio Selection," Operations Research, INFORMS, vol. 70(2), pages 815-829, March.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:2:p:815-829
    DOI: 10.1287/opre.2021.2197
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