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 abstract describes a paper that generalizes the Poisson process to a renewal process, especially Erlang (n) renewal processes.

Description: In this expository paper several comments are made with respect to the statistical independence of the curtate future lifetime and the fractional part of the future lifetime, both of a general status. In particular, the conditions for independence need to be stated carefully. The last-survivor status is cited as an example. More general assumptions than the uniform distribution of deaths assumption are then considered, together with applications to insurances, annuities, and reserves. Similar results to those under the uniform distribution of deaths assumption are obtained. Brief comments are made with respect to contingent probabilities in multiple lives and multiple decrement theory.

Description: This paper considers the distribution of aggregate claims of an insurer. The general form of the distribution is considered initially, and, after a few mild restrictions are imposed, it is characterized as being a compound distribution. Followed by one submitted discussion paper.

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: This paper represents an attempt to formulate a cohesive and consistent approach to the analysis of claim liabilities. Probabilistic tools from risk and queuing theory have been incorporated into a stochastic model that quantifies the variability inherent in such liabilities and at the same time reproduces intuitive results that may be arrived at from a deterministic standpoint.

Description: This paper represents an attempt to formulate a cohesive and consistent approach to the analysis of claim liabilities. Numerical examples are used to illustrate the methodology. From the Actuarial Research Clearing House ARCH 1990 Vol. 1.

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.

Description: This abstract describes a paper that obtains a closed-form expression for ruin quantity.

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.