Optimal Investment, Heterogeneous Consumption, and Best Time for Retirement

Hyun Jin Jang (), Zuo Quan Xu () and Harry Zheng ()
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Hyun Jin Jang: School of Business Administration, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
Zuo Quan Xu: Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
Harry Zheng: Department of Mathematics, Imperial College, London SW7 2BZ, United Kingdom

Operations Research, 2024, vol. 72, issue 2, 832-847

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 nonhomothetic 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 and 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 a partial differential equation 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: Stochastic Models; heterogeneous consumption; nonconcave utility; dynamic programming; optimal stopping; variational inequality; dual transformation; free boundary problem (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:72:y:2024:i:2:p:832-847

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