Optimal Investment, Heterogeneous Consumption and Best Time for Retirement

49 Pages Posted: 14 Jun 2022

See all articles by Hyun Jin Jang

Hyun Jin Jang

Ulsan National Institute of Science and Technology (UNIST)

Zuo Quan Xu

Hong Kong Polytechnic University

Harry Zheng

Imperial College London - Mathematical Finance

Date Written: May 31, 2022

Abstract

This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of non-homothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from PDE and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures.

Keywords: Heterogeneous consumption; Non-concave utility; Dynamic programming; Optimal stopping; Variational inequality; Dual transformation; Free boundary

JEL Classification: C02; C61

Suggested Citation

Jang, Hyun Jin and Xu, Zuo Quan and Zheng, Harry, Optimal Investment, Heterogeneous Consumption and Best Time for Retirement (May 31, 2022). Available at SSRN: https://ssrn.com/abstract=4123773 or http://dx.doi.org/10.2139/ssrn.4123773

Hyun Jin Jang (Contact Author)

Ulsan National Institute of Science and Technology (UNIST) ( email )

gil 50
Ulsan, 689-798
Korea, Republic of (South Korea)

Zuo Quan Xu

Hong Kong Polytechnic University ( email )

Harry Zheng

Imperial College London - Mathematical Finance ( email )

United Kingdom

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