Mean-field approximations in insurance
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 model, 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 counterpart, 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.
Keywords
Cite
@article{arxiv.2511.04198,
title = {Mean-field approximations in insurance},
author = {Philipp C. Hornung},
journal= {arXiv preprint arXiv:2511.04198},
year = {2026}
}