Consumption-leisure-investment strategies with time-inconsistent preference in a life-cycle model. Issue 24 (16th December 2020)

• Record Type: Journal Article
• Authors: Zhao, Qian; Siu, Tak Kuen
• Is Part Of: Communications in statistics. Volume 49:Issue 24(2020)
• Page Start: 6057
• Page End: 6079
• Publication Date: 2020-12-16
• Subjects: Labor flexibility -- life-cycle model -- non-exponential discounting -- time-inconsistence -- equilibrium strategies -- extended HJB equation; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1626426
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: This paper investigates a consumption-leisure-investment problem, where the object of an economic agent is to maximize the expected value of discounted lifetime utility in a life-cycle model. The agent is allowed to have considerable labor flexibility and the date of retirement is fixed. To incorporate some well-documented behavioral features of human beings, we consider the situation where the discounting is non-exponential. This situation is far from trivial and renders the optimization problem of the agent to be a nonstandard one, namely, a time-inconsistent stochastic control problem. The extended HJB equation for the time-inconsistent control problem is given. A verification theorem is proved for a general discount function and a general utility function. Explicit-form solutions are presented for the logarithmic utility with exponential discounting, pseudo-exponential discounting and hyperbolic discounting.