Linear Risk Sharing in Community-Based Insurance: Ruin Reduction in the Compound Poisson Model

TL;DR

This paper analyzes how proportional risk sharing in community-based insurance can reduce ruin probabilities for participants, providing conditions under which pooling benefits all members and illustrating the results with numerical examples.

Contribution

It establishes sufficient conditions for risk pooling to improve individual solvency and clarifies when pooling may not be beneficial, using convex-order comparisons.

Findings

Pooling reduces ruin probability under specific conditions.

Actuarial fairness and bounded transfers are key for benefits.

Numerical examples support theoretical conditions.

Abstract

This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cram\'er-Lundberg surplus process, and, whenever a claim is reported within the pool, its cost is redistributed according to a fixed allocation matrix. We compare the infinite-time ruin probability of each participant under stand-alone operation and under pool participation. Our main result shows that pooling reduces, for every participant, the infinite-time ruin probability when claim severities belong to a common scale family, the allocation rule satisfies full allocation and actuarial fairness, and each transfer remains bounded by an individual capacity condition. The proof relies on a convex-order comparison between the losses borne inside the pool and the corresponding stand-alone losses. We also clarify the role of these assumptions by showing that, outside this framework, pooling need not be beneficial for all participants. Numerical illustrations with Exponential and LogNormal severities support the theoretical findings and highlight how the design of proportional sharing rules affects solvency. The paper thus provides simple and interpretable sufficient conditions under which transparent linear risk-sharing arrangements improve individual solvency in community-based insurance.