# On Approximating Ruin Probability of Double Stochastic Compound Poisson Processes

## TL;DR

This paper develops two mixture exponential approximations for the ruin probability of a surplus process driven by two independent compound Poisson processes, with applications to bonus-malus systems and heavy-tailed claims.

## Contribution

It introduces novel mixture exponential formulas for ruin probability in double stochastic compound Poisson processes, improving upon classical bounds.

## Key findings

- Derived two approximation formulas for ruin probability
- Applied formulas to bonus-malus systems and heavy-tailed claims
- Showed improvements over Cramer-Lundberg bounds

## Abstract

Consider a surplus process which both of collected premium and payed claim size are two independent compound Poisson processes. This article derives two approximated formulas for the ruin probability of such surplus process, say double stochastic compound poisson process. More precisely, it provides two mixture exponential approximations for ruin probability of such double stochastic compound poisson process. Applications to long_term Bonus_Malus systems and a heavy-tiled claim size distribution have been given. Improvement of our findings compared to the Cramer- Lundberg upper bound has been given