Description: This paper presents an approach in which a defective renewal equation is solved in terms of a related compound geometric distribution. The advantage of this approach is discussed. The authors then apply this approach to a defective renewal equation which involves the time of ruin, the surplus before ruin and the total deficit at the time of ruin. They show how to compute the moments of the time of ruin as well as the joint distribution of the surplus before ruin and the deficit at the time of ruin. Two important cases in terms of claim size distributions are considered in detail. First, the authors consider exponential claim size distributions. They then consider a combination of two exponentials. The moments of the time of ruin are given in both cases.

Description: This is the abstract of an article about the classical Lundberg inequality of insurance risk theory. From ACTUARIAL RESEARCH CLEARING HOUSE 1994 VOL. 1.

Description: This is the abstract for the referenced paper on the subject of Lundberg bounds on the tails of compound distributions. From ACTUARIAL RESEARCH CLEARING HOUSE 1980 VOL. 2.