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Document Details : Title: A Note on Random Survivorship Group Benefits Author(s): RAMSAY, Colin M. Journal: ASTIN Bulletin Volume: 23 Issue: 1 Date: May 1993 Pages: 149-156 DOI: 10.2143/AST.23.1.2005106 Abstract : Consider a group of n independent lives age x where each life puts ยง 1 in a fund at time 0. The fund earns interest at rate t, and at the end of t years the accumulated value of the fund is divided equally among the survivors. The traditional approach to calculating the expected lump sum benefit per survivor from the initial group of n lives is based on the concept of a deterministic survivorship group This approach ignores the stochastic nature of the survivorship process. In reahty, the benefit per survivor is actually a random variable with an expected value which depends on the first inverse moment of a positive binomial random variable. Using GRAB'S and SAVAGE'S (1954) recursive formula for the first reverse moment, it is shown that the traditional approach yields a fairly accurate approximation to the solution even when one assumes a random number of survivors. |
