Optimal Investing after Retirement Under Time-Varying Risk Capacity Constraint

37 Pages Posted: 22 Jun 2020

See all articles by Weidong Tian

Weidong Tian

University of North Carolina (UNC) at Charlotte - The Belk College of Business Administration

Zimu Zhu

University of Southern California

Date Written: May 28, 2020

Abstract

This paper explores an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the optimal investing problem as an optimal portfolio choice problem under a time-varying risk capacity constraint. Under the specific condition on model parameters, we show that the value function is a $C^2$ solution of the HJB equation and derive the optimal investment strategy in terms of second-order ordinary differential equations. The optimal portfolio is nearly neutral to the stock market movement if the portfolio's value is at a sufficiently high level; but, if the portfolio is not worth enough to sustain the retirement spending, the retiree actively invests in the stock market for the higher expected return. In addition, we solve an optimal portfolio choice problem under a leverage constraint and show that the optimal portfolio would lose significantly in stressed markets. This paper shows that the time-varying risk capacity constraint has important implications for asset allocation in retirement.

Keywords: Risk Capacity, Retirement Portfolio, Longevity Risk, Leverage Constraint

JEL Classification: G11, G12, G13, D52, and D90

Suggested Citation

Tian, Weidong and Zhu, Zimu, Optimal Investing after Retirement Under Time-Varying Risk Capacity Constraint (May 28, 2020). Available at SSRN: https://ssrn.com/abstract=3612488 or http://dx.doi.org/10.2139/ssrn.3612488

Weidong Tian

University of North Carolina (UNC) at Charlotte - The Belk College of Business Administration ( email )

9201 University City Boulevard
Charlotte, NC 28223-0001
United States

HOME PAGE: http://belkcollegeofbusiness.uncc.edu/wtian1/

Zimu Zhu (Contact Author)

University of Southern California ( email )

3620 S Vermont Ave
KAP 104
Los Angeles, CA California 90089
United States

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