Optimal Retirement Choice under Age-dependent Force of Mortality

Giorgio Ferrari and Shihao Zhu
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Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Shihao Zhu: Center for Mathematical Economics, Bielefeld University

No 683, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with a random time horizon, featuring three state variables: wealth, labor income, and force of mortality. To address this problem, we transform it into its dual form, which is a finite time horizon, three-dimensional degenerate optimal stopping problem with interconnected dynamics. We establish the existence of an optimal retirement boundary that splits the state space into continuation and stopping regions. Regularity of the optimal stopping value function is derived and the boundary is proved to be Lipschitz continuous, and it is characterized as the unique solution to a nonlinear integral equation, which we compute numerically. In the original coordinates, the agent thus re- tires whenever her wealth exceeds an age-, labor income- and mortality-dependent transformed version of the optimal stopping boundary. We also provide numerical illustrations of the optimal strategies, including the sensitivities of the optimal retirement boundary concerning the relevant model’s parameters.

Keywords: Optimal retirement time; Optimal consumption; Optimal portfolio choice; Duality; Optimal stopping; Free boundary; Stochastic control (search for similar items in EconPapers)
Pages: 57
Date: 2023-11-21
New Economics Papers: this item is included in nep-age
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https://pub.uni-bielefeld.de/download/2984621/2984622 First Version, 2023 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:683

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