Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-23T23:54:44.039Z Has data issue: false hasContentIssue false
  • English
  • Français

On Simple Ruin Expressions in Dependent Sparre Andersen Risk Models

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

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Adan, I. J. B. F. and Kulkarni, V. G. (2003). Single-server queue with Markov-dependent inter-arrival and service times. Queueing Systems 45, 113–134.Google Scholar
Ahn, S. and Badescu, A. L. (2007). On the analysis of the Gerber–Shiu discounted penalty function for risk processes with Markovian arrivals. Insurance Math. Econom. 41, 234–249.Google Scholar
Albrecher, H. and Boxma, O. J. (2004). A ruin model with dependence between claim sizes and claim intervals. Insurance Math. Econom. 35, 245–254.Google Scholar
Albrecher, H. and Boxma, O. J. (2005). On the discounted penalty function in a Markov-dependent risk model. Insurance Math. Econom. 37, 650–672.Google Scholar
Albrecher, H. and Teugels, J. L. (2006). Exponential behavior in the presence of dependence in risk theory. J. Appl. Prob. 43, 257–273.CrossRefGoogle Scholar
Asmussen, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.Google Scholar
Asmussen, S. and Albrecher, H. (2010). Ruin Probabilities, 2nd edn. World Scientific, Hackensack, NJ.Google Scholar
Boudreault, M., Cossette, H., Landriault, D. and Marceau, E. (2006). On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actuarial J. 2006, 265–285.Google Scholar
Breuer, L. (2008). First passage times for Markov additive processes with positive Jumps of phase type. J. Appl. Prob. 45, 779–799.CrossRefGoogle Scholar
Cheung, E. C. K., Landriault, D. and Badescu, A. L. (2011). On a generalization of the risk model with Markovian claim arrivals. Stoch. Models 27, 407–430.Google Scholar
Cheung, E. C. K., Landriault, D., Willmot, G. E. and Woo, J.-K. (2010). Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models. Insurance Math. Econom. 46, 117–126.CrossRefGoogle Scholar
D'Auria, B., Ivanovs, J., Kella, O. and Mandjes, M. (2010). First passage of a Markov additive process and generalized Jordan chains. J. Appl. Prob. 47, 1048–1057.Google Scholar
Horn, R. A. and Johnson, C. R. (1990). Matrix Analysis. Cambridge University Press.Google Scholar
Ivanovs, J. (2013). A note on killing with applications in risk theory. Insurance Math. Econom. 52, 29–34.Google Scholar
Kwan, I. K. M. and Yang, H. (2007). Ruin probability in a threshold insurance risk model. Belg. Actuarial Bull. 7, 41–49.Google Scholar