Valuation of guaranteed lifelong withdrawal benefit with the long-term care option

Yang Yang, Shaoying Chen, Zhenyu Cui and Zhimin Zhang

Insurance: Mathematics and Economics, 2024, vol. 119, issue C, 179-193

Abstract: In this paper, under the stochastic interest rate framework, we consider the valuation of a Guaranteed Lifelong Withdrawal Benefit (GLWB) annuity product by explicitly incorporating the health state of the policyholder through the long-term care (LTC) option. The product provides policyholders with protection against longevity risk and market downturns, as well as financial support when facing LTC needs. Within the context of dynamic withdrawals, the valuation of the GLWB annuity with the LTC option is characterized as a stochastic optimal control problem. We introduce a novel bang-bang analysis approach without the usual convexity assumption in literature and prove that the optimal withdrawal strategies for the policyholder are constrained to a finite set. Furthermore, we perform a sensitivity analysis on the price determinants of GLWB annuities with and without the LTC option, and provide economic interpretations. Lastly, we investigate the impact of gender on the optimal withdrawal strategy and the fair fee of the annuity with the LTC option.

Keywords: Long-term care; Variable annuities; Bang-bang analysis; Optimal control (search for similar items in EconPapers)
JEL-codes: C61 G13 G22 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:119:y:2024:i:c:p:179-193

DOI: 10.1016/j.insmatheco.2024.09.001

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