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Mathematical Fun with the Compound Binomial Process

Published online by Cambridge University Press:  29 August 2014

Hans U. Gerber
Hans U. Gerber*
Affiliation:
Université de Lausanne
*
Ecole des H.E.C., Université de Lausanne, 1015 Lausanne, Switzerland
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Abstract

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The compound binomial model is a discrete time analogue (or approximation) of the compound Poisson model of classical risk theory. In this paper, several results are derived for the probability of ruin as well as for the joint distribution of the surpluses immediately before and at ruin. The starting point of the probabilistic arguments are two series of random variables with a surprisingly simple expectation (Theorem 1) and a more classical result of the theory of random walks (Theorem 2) that is best proved by a martingale argument.

Keywords

Ruinbinomial modelcompound binomial processbonus malusseverity of ruin
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 18 , Issue 2 , November 1988 , pp. 161 - 168
Copyright
Copyright © International Actuarial Association 1988

References

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