Description: Random sum models with compound distributions are used extensively in modeling of insurance risks. Unfortunately, the compound distributions themselves are awkward to evaluate. Consequently, various numerical and analytical approximative techniques have been used. In this talk we derive various upper and lower bounds on the tails of compound distributions. Some notions in reliability theory are used.

Description: In a series papers by Willmot and Lin, both exponential and non-exponential bounds for the tail probability of various compound distributions have been derived. In Wilmot, it was suggested that non-exponential bounds for the ruin probability were difficult to obtain using martingale arguments. In this note, we show how to use martingale inequalities to obtain some upper bounds for the ruin probability.