Valuation and Asset-Liability Management of Ratchet Life Insurances with Backward Stochastic Differential Equations
(2026) , 31 pages
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- Abstract
- This article develops a valuation and asset-liability management framework for ratchet life insurance contracts with survival and death benefits, in the presence of stochastic financial and mortality risks. The insured benefits combine a unit-linked investment component with periodically updated guaranteed minimum benefits, creating embedded path-dependent options and longevity exposure. Financial markets are modeled through correlated stochastic processes for equity returns and interest rates, while mortality intensity follows a mean-reverting Gaussian process. The fair value of liabilities is formulated under the risk-neutral measure and characterized through a backward stochastic differential equation (BSDE) with jump components associated with deaths in the insured population. We derive the corresponding Feynman–Kac representation and obtain explicit expressions for survival probabilities and the mortality swap. The BSDE formulation naturally provides both liability value and dynamic hedging strategies against equity, interest-rate, and mortality risks. Numerical valuation is performed using a Least-Squares Monte-Carlo (LSMC) algorithm adapted to the jump-diffusion setting. The proposed methodology delivers a tractable framework for pricing and hedging life insurance liabilities with ratchet guarantees under stochastic mortality.
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Citations
Hainaut, D. (2026). Valuation and Asset-Liability Management of Ratchet Life Insurances with Backward Stochastic Differential Equations (LIDAM Discussion Paper ISBA 2026/35). https://hdl.handle.net/2078.5/281483