Ruin Probabilities in a Markovian Shot-Noise Environment
Probability
2022-05-11 v1
Abstract
We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cram\'er-Lundberg model, namely the constant jump intensity of the Poisson process. Due to this structure, we can apply the theory of PDMPs on a multivariate process containing the intensity and the reserve process, which allows us to identify a family of martingales. Eventually, we use change of measure techniques to derive an upper bound for the ruin probability in this model. Exploiting a recurrent structure of the shot-noise process, even the asymptotic behaviour of the ruin probability can be determined.
Cite
@article{arxiv.2205.04896,
title = {Ruin Probabilities in a Markovian Shot-Noise Environment},
author = {Simon Pojer and Stefan Thonhauser},
journal= {arXiv preprint arXiv:2205.04896},
year = {2022}
}