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 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: 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.

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.