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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

REFERENCES

Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1986) Actuarial Mathematics. Society of Actuaries, Itasca, IL.Google Scholar
Govindarajulu, Z. (1963) “Recurrence relations for the inverse moments of the positive binomial variable”. Journal of the American Statistical Association 58, 468–473.CrossRefGoogle Scholar
Grab, E.L. and Savage, I.R. (1954) “Tables of the expected value of 1/X for positive Bernouilli and Poisson variables”. Journal of the American Statistical Association 49, 169–177.Google Scholar
Ling, R.F. (1992) “Just say no to binomial (and other discrete distributions) Tables”. The American Statistician 46, No. 1, 53–54.Google Scholar
Mendenhall, W. and Lehman, E.H. Jr. (1960) “An approximation to the negative moments of the positive binomial useful in life testing”. Technometrics 2, No. 2, 227–242.CrossRefGoogle Scholar
Neill, A. (1977) Life Contingencies. Heinemann, London.Google Scholar
Walker, J.J. (1984) “Improved approximations for the inverse moments of the positive binomial distribution”. Communications in Statistics: Simulations and Computations 13, No. 4, 515–519.CrossRefGoogle Scholar