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Large deviations for risk processes with reinsurance

Part of: Limit theorems Mathematical economics Applications

Published online by Cambridge University Press:  14 July 2016

Claudio Macci  and
Gabriele Stabile
Claudio Macci*
Affiliation:
Università di Roma ‘Tor Vergata’
Gabriele Stabile*
Affiliation:
Università di Roma ‘La Sapienza’
*
∗Postal address: Dipartimento di Matematica, Università di Roma ‘Tor Vergata’, Via della Ricerca Scientifica, I-00133 Rome, Italy. Email address: [email protected]
∗∗Postal address: Dipartimento di Matematica per le Decisioni Economiche Finanziarie ed Assicurative, Università di Roma ‘La Sapienza’, Via del Castro Laurenziano 9, I-00161 Rome, Italy. Email address: [email protected]
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Abstract

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We consider risk processes with reinsurance. A general family of reinsurance contracts is allowed, including proportional and excess-of-loss policies. Claim occurrence is regulated by a classical compound Poisson process or by a Markov-modulated compound Poisson process. We provide some large deviation results concerning these two risk processes in the small-claim case. Finally, we derive the so-called Lundberg estimate for the ruin probabilities and present a numerical example.

Keywords

Large deviationsrisk processreinsuranceruin probabilityLundberg estimate

MSC classification

Primary: 60F10: Large deviations 91B30: Risk theory, insurance 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 713 - 728
Copyright
© Applied Probability Trust 2006 

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