In this paper we compare ruin 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 in the Markov modulated model and the distribution of the claim size is obtained by averaging the ones over consecutive claim sizes.
