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A Note on Random Survivorship Group Benefits

Published online by Cambridge University Press:  29 August 2014

Colin M. Ramsay
Colin M. Ramsay*
Affiliation:
University of Nebraska, 310 Burnett Hall Lincoln, NE, USA68588-0307 (402)-472-5823
*
University of Nebraska, 310 Burnett Hall, Lincoln, NE, USA68588-0307, (402)-472-5823.
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Abstract

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Consider a group of n independent lives age x where each life puts § 1 in a fund at time 0. The fund earns interest at rate i, 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 reality, 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 inverse 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.

Keywords

Inverse momentspositive binomial distributionactuarial accumulated value
Type
Short Contributions
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 1 , May 1993 , pp. 149 - 156
Copyright
Copyright © International Actuarial Association 1993

References

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