Description: This paper studies the tail probability of discounted aggregate claims in a continuous-time renewal model. For the case that the common claim-size distribution is subexponential, the authors obtain an asymptotic formula, which holds uniformly for all time horizons within a finite interval. Then, with some additional mild assumptions on the distributions of the claim sizes and inter-arrival times, the authors further prove that this formula holds uniformly for all time horizons.

Description: This report describes a stochastic simulation approach used to estimate the amount of a level-payment annuity payable as long as the person is alive and living in his/her house. A discussion of the paper follows. From Transactions of Society of Actuaries 1991, Vol. 43.