Paper: arXiv 2511.04198

Authors: 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 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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents high-level mathematical rigor, establishing total variation chaos and convergence proofs for McKean-Vlasov Markov jump processes applied to insurance liabilities. However, it is entirely theoretical with illustrative stylized network examples rather than empirical data validation or backtesting.

Research Flowchart

  flowchart TD
    A[Goal: Calculate Insurance Liabilities for Large Dependent Cohorts] --> B[Input: Coupled High-Dimensional Linear Integro-Differential Equations]
    B --> C[Problem: Infeasible Computation for Large Cohorts]
    C --> D[Method: Apply Mean-Field Approximation & Jump Processes]
    D --> E[Process: Replace High-Dim System with Low-Dim Non-Linear Equations]
    E --> F[Validation: Prove Convergence as Cohort Size Approaches Infinity]
    F --> G[Outcome: Feasible Liability Calculation for Life & Non-Life Insurance]

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0 of 37 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.