On the ordering of ruin probabilities for the surplus process perturbed by diffusion

In this paper, we study orders of pairs of ruin probabilities resulting from two individual claim size random variables for corresponding continuous time surplus processes perturbed by diffusion with different premium rates, relative security loadings, and variance parameters of the diffusion processes. We show that high frequency and low severity risks yield smaller ruin probabilities than low frequency and high severity risks. These ordering relationships can also be used to obtain upper and/or lower bounds on ruin probabilities. Finally, some examples are given to illustrate the results of the theorems.