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Moderate- and large-deviation probabilities in actuarial risk theory

Published online by Cambridge University Press:  01 July 2016

Eric Slud  and
Craig Hoesman
Eric Slud*
Affiliation:
University of Maryland
Craig Hoesman*
Affiliation:
U.S. Department of Defence
*
∗Postal address: Statistics Program, Mathematics Department, University of Maryland, College Park, MD 20742, USA.
∗∗Permanent address: Special U.S. Liaison Officer, Box 5000, U.S. Embassy, Ogdensburg, NY 13669-0430, USA.
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Abstract

A general model for the actuarial risk-reserve process as a superposition of compound delayed-renewal processes is introduced and related to previous models which have been used in collective risk theory. It is observed that non-stationarity of the portfolio ‘age-structure' within this model can have a significant impact upon probabilities of ruin. When the portfolio size is constant and the policy age-distribution is stationary, the moderate- and large-deviation probabilities of ruin are bounded and calculated using the strong approximation results of Csörg et al. (1987a, b) and a large-deviation theorem of Groeneboom et al. (1979). One consequence is that for non-Poisson claim-arrivals, the large-deviation probabilities of ruin are noticeably affected by the decision to model many parallel policy lines in place of one line with correspondingly faster claim-arrivals.

Keywords

RISK-RESERVE PROCESSCOMPOUND DELAYED-RENEWAL PROCESSSUPERPOSITIONSTRONG APPROXIMATION
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 725 - 741
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Research supported by Office of Naval Research under contract ONR-86-K-0007.

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