Ruin under stochastic dependence between premium and claim arrivals

TL;DR

This paper analyzes an adapted Cramer-Lundberg model where the premium and claim arrivals are conditionally independent given their intensities, leading to a stochastic dependence between aggregate premium and claim processes, with explicit ruin probability formulas for exponential sizes.

Contribution

It introduces a novel model capturing stochastic dependence between premiums and claims and derives explicit ruin probability expressions for exponential distributions.

Findings

Explicit ruin probability formula derived for exponential claim and premium sizes.

Model captures stochastic dependence between premium and claim processes.

Provides analytical tools for risk assessment under dependence structures.

Abstract

We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the arrival times of the premiums and of the claims respectively, are independent. Such a model exhibits a stochastic dependence between the aggregate premium and claim amount processes. An explicit expression for the ruin probability is obtained when the claim and premium sizes are exponentially distributed.