Does Markov-Modulation Increase the Risk?

In this paper we compare rum functions for two risk processes with respect to stochastic ordering, stop-loss ordering and ordering of adjustment coefficients. The risk processes are as follows, in the Markov-modulated environment and the associated averaged compound Poisson model. In the latter case the arrival rate is obtained by averaging over time the arrival rate m the Markov modulated model and the distribution of the claim size is obtained by averaging the ones over consecutive claim sizes. Keywords: Risk theory, compound Poisson model, Markov environment, stochastic ordering, stop-loss ordering, adjustment coefficient, exponential tad ordering, perturbation.