Nonlinear reserving in life insurance: Aggregation and mean-field approximation

Boualem Djehiche and Björn Löfdahl

Insurance: Mathematics and Economics, 2016, vol. 69, issue C, 1-13

Abstract: We suggest a unified approach to claims reserving for life insurance policies with reserve-dependent payments driven by multi-state Markov chains. The associated prospective reserve is formulated as a recursive utility function using the framework of backward stochastic differential equations (BSDE). We show that the prospective reserve satisfies a nonlinear Thiele equation for Markovian BSDEs when the driver is a deterministic function of the reserve and the underlying Markov chain. Aggregation of prospective reserves for large and homogeneous insurance portfolios is considered through mean-field approximations. We show that the corresponding prospective reserve satisfies a BSDE of mean-field type and derive the associated nonlinear Thiele equation.

Keywords: Backward stochastic differential equation; Life insurance; Multistate models; Markov process; Mean-field; Surrender value; Thiele’s equation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:69:y:2016:i:c:p:1-13

DOI: 10.1016/j.insmatheco.2016.04.002

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