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arXiv · 2311.12169

Optimal Retirement Choice under Age-dependent Force of Mortality

Giorgio Ferrari·Shihao Zhu
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Abstract

This paper examines optimal investment, consumption, and retirement timing 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 wealth, labor income, and the force of mortality. To address this problem, we transform it into its dual form, which is a finite time horizon, three-dimensional optimal stopping problem with joint dynamics. We establish the existence of an optimal retirement boundary that separates the state space into continuation and stopping regions. We derive regularity of the optimal stopping value function, prove that the dual boundary is locally Lipschitz, and characterize the boundary as the unique solution to a nonlinear integral equation, which is solved numerically. In the original coordinates, the agent retires whenever her wealth exceeds an age- , labor-income-, and force-of-mortality-dependent transformation of the optimal stopping boundary. We also provide numerical illustrations of the optimal strategies, including sensitivity analyses of the optimal retirement boundary with respect to the relevant model parameters.

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Giorgio Ferrari, Shihao Zhu. 2023-11-20. Optimal Retirement Choice under Age-dependent Force of Mortality. https://arxiv.org/abs/2311.12169

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