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

Alain Bensoussan (), SingRu (Celine) Hoe (), Joohyun Kim () and Zhongfeng Yan ()
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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

Operations Research, 2022, vol. 70, issue 2, 815-829

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.

Keywords: Financial Engineering; consumption and portfolio choice; risk management; mean field-type control; fixed point problem; time inconsistency (search for similar items in EconPapers)
Date: 2022
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