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Time-varying pareto optimal risk sharing for annuities

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  • Hanbali, Hamza
  • Warnakulasooriya, Himasha
  • Leung, Jessica Wai Yin

Abstract

This paper investigates time-varying risk sharing between annuity buyer and provider. It explores Pareto optimal (PO) and viable Pareto optimal (VPO) risk-sharing designs, in which the share of the reserve deviation transferred to the policyholder varies over time. The optimization problem, based on a weighted average of mean-variance preferences, results in a complex quartic objective function. Such optimization problems are difficult to solve, and checking their convexity is known to be NP-hard. A heuristic method is introduced to simplify the problem, providing a closed-form solution that closely approximates the numerical results. The paper also highlights factors influencing the existence of VPO designs, with age playing a critical role, thereby suggesting the suitability of these designs as retirement products.

Suggested Citation

  • Hanbali, Hamza & Warnakulasooriya, Himasha & Leung, Jessica Wai Yin, 2025. "Time-varying pareto optimal risk sharing for annuities," ASTIN Bulletin, Cambridge University Press, vol. 55(3), pages 695-720, September.
    • Handle: RePEc:cup:astinb:v:55:y:2025:i:3:p:695-720_10
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