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Retirement Decision with Addictive Habit Persistence in a Jump Diffusion Market

Year: 2025

Type: article

Abstract: . This paper investigates the optimal retirement decision, investment, and consumption strategies in a market with jump diffusion, taking into account habit persistence and stock-wage correlation. Our analysis considers multiple stocks and a finite time framework, intending to determine the retirement boundary of the “wealth-habit-wage” triplet [Formula: see text]. To achieve this, we use the habit reduction method and a duality approach to obtain the retirement boundary of the primal variables and feedback forms of optimal strategies. When dealing with the dual problem, we address technical challenges in the proof of integral equation characterization of optimal retirement boundary using a [Formula: see text] version of It[Formula: see text]’s formula. Our results show that when the so-called de facto wealth exceeds a critical proportion of wage, an immediate retirement is the optimal choice for the agent. Additionally, we find that the introduction of jump risks allows for the possibility of discontinuous investment strategies within the working region, which is a novel and insightful finding. Our numerical results effectively illustrate these findings by varying the parameters.

Source: SIAM Journal on Financial Mathematics

DOI: 10.1137/23m1591116

Authors: Guohui Guan, Qitao Huang, Zongxia Liang, Fengyi Yuan

Institutions: Renmin University of China, Tsinghua University, University of Michigan

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

SDG: Decent work and economic growth

Open Access status: green

Funder: National Natural Science Foundation of China