On a Generalization of the Risk Model with Markovian Claim Arrivals

Abstract

The class of risk models with Markovian arrival process (MAP) (see e.g., Neuts[ 15 ]) is generalized by allowing the waiting times between two successive events (which can be a change in the environmental state and/or a claim arrival) to have an arbitrary distribution. Using a probabilistic approach, we determine the solution for a class of Gerber–Shiu functions apart from some unknown constants when claim sizes have a mixed exponential distribution. Such constants are later determined using the more classic ruin-analytic approach. A numerical example is later considered to illustrate the tractability of the suggested methodology in the study of Gerber–Shiu functions.