关键词: Homogeneous Markov process, ruin probability, deficit, duration of negative surplus, compound Poisson risk model

Abstract:

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of
exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

Key words: Homogeneous Markov process, ruin probability, deficit, duration of negative surplus, compound Poisson risk model