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Optimal Retirement Choice under Age-dependent Force of Mortality

Author

Listed:
  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Zhu, Shihao

    (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.

Suggested Citation

  • Ferrari, Giorgio & Zhu, Shihao, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Center for Mathematical Economics Working Papers 683, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:683
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    References listed on IDEAS

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    Keywords

    Optimal retirement time; Optimal consumption; Optimal portfolio choice; Duality; Optimal stopping; Free boundary; Stochastic control;
    All these keywords.

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