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Mean-field approximations in insurance

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  • Philipp C. Hornung

Abstract

The calculation of the insurance liabilities of a cohort of dependent individuals in general requires the solution of a high-dimensional system of coupled linear forward integro-differential equations, which is infeasible for a larger cohort. However, by using a mean-field approximation, the high dimensional system of linear forward equations can be replaced by a low-dimensional system of non-linear forward integro-differential equations. We show that, subject to certain regularity conditions, the insurance liability viewed as a (conditional) expectation of a functional of an underlying jump process converges to its mean-field approximation, as the number of individuals in the cohort goes to infinity. Examples from both life- and non-life insurance illuminate the practical importance of mean-field approximations.

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  • Philipp C. Hornung, 2025. "Mean-field approximations in insurance," Papers 2511.04198, arXiv.org.
    • Handle: RePEc:arx:papers:2511.04198
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