| This thesis generalized the concept of stop-loss transforms, an important concept in risk theory (6), to the nth stop-loss transforms. Some useful properties of the nth stop-loss transforms were discovered and a recursion formula for the nth stop-loss transforms was established. Also, the maintenance properties of the nth stop-loss order under convolution, compound and mixture operations were proved. Finally the results mentioned above were applied to the study of losses {dollar}Lsb{lcub}i{rcub} (i = 1,2,cdots),{dollar} maximal aggregate loss L and ruin probability {dollar}Tpsi(u).{dollar} Some inequalities for the expectation of {dollar}Lsb{lcub}i{rcub}{dollar} and L were given, and a relationship between the claim amount random variable and ruin probability was found. |
