A characterization of ruin-inducing probability measures in a renewal risk model

Spyridon M. Tzaninis; Apostolos Bozikas

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arXiv · 2604.24061

A characterization of ruin-inducing probability measures in a renewal risk model

Spyridon M. Tzaninis·Apostolos Bozikas

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Abstract

In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(\gamma,\delta)$. This result allows us to obtain an explicit representation of the infinite-time ruin probability as an expectation under any ruin-inducing probability measure. A key feature of our approach is that the construction of these measures does not rely on the existence of moment generating functions, and is therefore applicable to heavy-tailed claim size distributions. The proposed framework includes the classical Esscher transform as a special case.

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Spyridon M. Tzaninis, Apostolos Bozikas. 2026-04-27. A characterization of ruin-inducing probability measures in a renewal risk model. https://arxiv.org/abs/2604.24061

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