Mean-field approximations in insurance

Fuente: arXiv
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Main Author: Hornung, Philipp C.
Format: Preprint
Published: 2025
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author Hornung, Philipp C.
author_facet Hornung, Philipp C.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_04198
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Mean-field approximations in insurance
Hornung, Philipp C.
Risk Management
Probability
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.
title Mean-field approximations in insurance
topic Risk Management
Probability
url https://arxiv.org/abs/2511.04198