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

Author

Listed:
  • Yang, Yang
  • Chen, Shaoying
  • Cui, Zhenyu
  • Zhang, Zhimin

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.

Suggested Citation

  • Yang, Yang & Chen, Shaoying & Cui, Zhenyu & Zhang, Zhimin, 2024. "Valuation of guaranteed lifelong withdrawal benefit with the long-term care option," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 179-193.
    • Handle: RePEc:eee:insuma:v:119:y:2024:i:c:p:179-193
    DOI: 10.1016/j.insmatheco.2024.09.001
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    More about this item

    Keywords

    Long-term care; Variable annuities; Bang-bang analysis; Optimal control;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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