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Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes

Part of: Limit theorems Mathematical modeling, applications of mathematics Mathematical economics

Published online by Cambridge University Press:  16 July 2020

Hansjörg Albrecher ,
Bohan Chen ,
Eleni Vatamidou  and
Bert Zwart
Hansjörg Albrecher*
Affiliation:
University of Lausanne and Swiss Finance Institute
Bohan Chen*
Affiliation:
Centrum Wiskunde & Informatica (CWI)
Eleni Vatamidou*
Affiliation:
University of Lausanne
Bert Zwart*
Affiliation:
CWI and Eindhoven University of Technology
*
*Postal address: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, 1015 Lausanne, Switzerland.
**Postal address: Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.
*Postal address: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, 1015 Lausanne, Switzerland.
**Postal address: Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.
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Abstract

We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin after reinsurance is also regularly varying in terms of the initial capital, and derive an explicit asymptotic expression for the latter. We establish this result by leveraging recent developments on sample-path large deviations for heavy tails. Our results allow, on the asymptotic level, for an explicit comparison between two well-known large-claim reinsurance contracts, namely LCR and ECOMOR. Finally, we assess the accuracy of the resulting approximations using state-of-the-art rare event simulation techniques.

Keywords

finite-time ruin probabilitieslarge deviationsheavy tailslarge-claim reinsuranceECOMOR

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60F10: Large deviations 97M30: Financial and insurance mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 513 - 530
Copyright
© Applied Probability Trust 2020

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