A Risk Extended Version of Merton’s Optimal Consumption and Portfolio Selection
Alain Bensoussan, SingRu (Celine) Hoe, Joohyun Kim, Zhongfeng Yan
Operations Research · 2022 · Volume 70 · Issue 2
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
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