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On the Distribution of the Surplus Prior and at Ruin

Published online by Cambridge University Press:  29 August 2014

Hanspeter Schmidli
Hanspeter Schmidli*
Affiliation:
Department of Theoretical Statistics, Aarhus University
*
Department of Theoretical Statistics, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark
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Abstract

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Consider a classical compound Poisson model. The safety loading can be positive, negative or zero. Explicit expressions for the distributions of the surplus prior and at ruin are given in terms of the ruin probability. Moreover, the asymptotic behaviour of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cramer case, the case of subexponential distributions and some intermediate cases are discussed.

Keywords

Ruinasymptotic distributionchange of measureLaplace transformsubexponential distributionCramer conditiongeneralized Pareto distributionmaximum domain of attractionGumbel distribution
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 227 - 244
Copyright
Copyright © International Actuarial Association 1999

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