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On Simple Ruin Expressions in Dependent Sparre Andersen Risk Models

Part of: Mathematical economics Mathematical modeling, applications of mathematics Special processes

Published online by Cambridge University Press:  30 January 2018

Hansjörg Albrecher ,
Onno J. Boxma  and
Jevgenijs Ivanovs
Hansjörg Albrecher*
Affiliation:
University of Lausanne
Onno J. Boxma*
Affiliation:
Eindhoven University of Technology and EURANDOM
Jevgenijs Ivanovs*
Affiliation:
University of Lausanne
*
∗ Postal address: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland.
∗∗ Postal address: Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: o.j.boxma@tue.nl
∗ Postal address: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland.
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Abstract

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In this note we provide a simple alternative probabilistic derivation of an explicit formula of Kwan and Yang (2007) for the probability of ruin in a risk model with a certain dependence between general claim interoccurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probability expressions in more general risk models with dependence.

Keywords

Sparre Andersen risk modelruin probabilityMarkov additive process

MSC classification

Primary: 91B30: Risk theory, insurance 97M30: Financial and insurance mathematics 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 293 - 296
Copyright
© Applied Probability Trust 

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