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Bankruptcy probabilities under non-poisson inspection

Part of: Applications

Published online by Cambridge University Press:  19 March 2025

Florine Kuipers ,
Michel Mandjes  and
Sara Morcy
Florine Kuipers*
Affiliation:
University of Amsterdam
Michel Mandjes*
Affiliation:
Leiden University, University of Amsterdam
Sara Morcy*
Affiliation:
University of Amsterdam
*
*Postal address: Boston Consulting Group, Gustav Mahlerlaan 40, 1082 MC Amsterdam, The Netherlands. Email: [email protected]
**Postal address: Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands. Email: [email protected]
***Postal address: University of Amsterdam, Science Park 904 1098 XH Amsterdam, The Netherlands. Email: [email protected]
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Abstract

This paper concerns an insurance firm’s surplus process observed at renewal inspection times, with a focus on assessing the probability of the surplus level dropping below zero. For various types of inter-inspection time distributions, an explicit expression for the corresponding transform is given. In addition, Cramér–Lundberg-type asymptotics are established. Also, an importance sampling-based Monte Carlo algorithm is proposed, and is shown to be logarithmically efficient.

Keywords

Cramér–Lundberg modelperiodic inspectionlarge deviationsruin probabilityimportance sampling

MSC classification

Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 40
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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