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A finite-time ruin probability formula for continuous claim severities

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Zvetan G. Ignatov  and
Vladimir K. Kaishev
Zvetan G. Ignatov*
Affiliation:
Sofia University ‘St Kliment Ohridski’
Vladimir K. Kaishev*
Affiliation:
City University, London
*
∗ Postal address: Faculty of Economics and Business Administration, Sofia University ‘St Kliment Ohridski’, 125 Tsarigradsko Shosse Boulevard, bl. 3, Sofia 1113, Bulgaria.
∗∗ Postal address: Faculty of Actuarial Science and Statistics, Cass Business School, City University, 106 Bunhill Row, London EC1 8TZ, UK. Email address: [email protected]
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Abstract

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

Keywords

Risk processPoisson claim arrivalpremium-income functionclaim severities distributionfinite-time ruin probabilityAppell polynomial

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 570 - 578
Copyright
Copyright © Applied Probability Trust 2004 

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References

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