A risk model with an observer in a Markov environment
Probability
2013-10-14 v1
Abstract
We consider a spectrally-negative Markov additive process as a model of a risk process in random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.
Keywords
Cite
@article{arxiv.1310.3054,
title = {A risk model with an observer in a Markov environment},
author = {Hansjoerg Albrecher and Jevgenijs Ivanovs},
journal= {arXiv preprint arXiv:1310.3054},
year = {2013}
}