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An elementary proof of the Adelson-Panjer recursion formula. (English) Zbl 0657.62122
We present a new proof of the Adelson-Panjer recursion formula for computing discrete compound Poisson densities. It uses only elementary probability theory and elementary arithmetic.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
65C30 Numerical solutions to stochastic differential and integral equations
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References:
[1] Adelson, R.M., Compound Poisson distributions, Operations research quarterly, 17, 73-75, (1966)
[2] Gerber, H.U., Introduction to the mathematical theory of risk, (1980), The Huebner Foundation Philadelphia, PA
[3] Panjer, H.H., Recursive evaluation of a family of compound distributions, ASTIN bulletin, 12, 22-26, (1981)
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