Ruin under stochastic dependence between premium and claim arrivals

Abstract

We investigate, focusing on the ruin probability, an adaptation of the Cramér–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.

Keywords:

• Cramér–Lundberg model
• surplus process
• stochastic dependence
• probability of ruin

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author acknowledges financial support from the Slovenian Research Agency [research core funding number P1-0222]. He thanks the anonymous Referee: several meaningful points are made on his/her advice.