Compound binomial risk model in a markovian environment

Abstract

In this paper, we propose a compound binomial model defined in a markovian environment which is an extension to the compound binomial model presented by Gerber (1988) [Mathematical fun with the compound bionomial process. ASTIN Bull. 18, 109–123; Mathematical fun with ruin theory. Ins. Math. Econ. 7, 15–23]. An algorithm is presented for the computation of the aggregate claim amount distribution for a fixed time period. We focus on infinite-time ruin probabilities and propose a numerical algorithm to compute their numerical values. Along the same lines as Gerber’s compound binomial model which can be used as an approximation to the classical risk model, we will see that the compound binomial model defined in a markovian environment can approximate the risk model based on a particular Cox model, the marked Markov modulated Poisson process. Finally, we compare via stochastic ordering theory our proposed model to two other risk models: Gerber’s compound binomial model and a mixed compound binomial model. Numerical examples are provided.