| Some useful properties of the nth stop-loss order and the exponential order will be given in this paper. These results will be applied to the study of losses {dollar}Lsb{lcub}i{rcub}{dollar} (i = 1, 2,{dollar}cdots{dollar}), L and ruin probability {dollar}psi{dollar}(u). A relationship between the claim amount random variables and ruin probabilities will also be found. The concepts of the nth stop-loss distance and the ruin probability distance will be introduced. A formula for ruin probabilities for heterogeneous portfolios will be given. |
