Time-varying pareto optimal risk sharing for annuities

Hamza Hanbali, Himasha Warnakulasooriya and Jessica Wai Yin Leung

ASTIN Bulletin, 2025, vol. 55, issue 3, 695-720

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.

Date: 2025
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