Hostname: page-component-6d856f89d9-vrt8f Total loading time: 0 Render date: 2024-07-16T04:40:28.187Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Distribution of the Surplus Prior to Ruin in a Discrete Semi-Markov Risk Model

Published online by Cambridge University Press:  29 August 2014

J.M. Reinhard  and
M. Snoussi
J.M. Reinhard*
Affiliation:
Université Libre de Bruxelles
M. Snoussi*
Affiliation:
Université Libre de Bruxelles Secura Belgian Re, Belgique
*
Secura s.a., Montoyer, 12, B-1000 Bruxelles, Belgique
Université Libre de Bruxelles, Campus de la plaine CP 210, B-1050 Bruxelles, Belgique
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 paper we extend the work of Reinhard and Snoussi (2000) by developing a recursive system for finding the distribution of the surplus prior to ruin in a discrete semi-Markov risk model.

Keywords

Probability of ruinsurplus prior to ruinrecursive calculationstable algorithm
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 2 , November 2001 , pp. 255 - 273
Copyright
Copyright © International Actuarial Association 2001

References

Asmussen, S. (1989). Risk theory in a markovian environment. Scand. Actuarit J., 66–100.Google Scholar
Bowers, N.L., Gerber, H.V., Hickman, J.C., Jones, , D.A. and Nesbitt, C.J. (1987). Actuarial Mathematics. Society of Actuaries, Itasca, Illinois.Google Scholar
Dickson, D.C.M. (1992). On the distribution of the surplus prior to ruin. Insurance: Mathematics and Economics 11, 191–207.Google Scholar
Dickson, D.C.M. and Waters, H.R. (1992). The probability and severity of ruin in finite and infinite time. Astin Bulletin 23, 177–190.CrossRefGoogle Scholar
Dickson, D.C.M., Egidio Dos Reis, A.D. and Waters, H.R. (1995). Some stable algorithms in ruin theory and their applications. Astin Bulletin 25, 153–175.CrossRefGoogle Scholar
Dufresne, F. (1989). Probabilité et sévérité de la ruine modèle classique de la théorie du risque collectif et une de ses extensions. Ph.D. thesis, Université de Lausanne.Google Scholar
Dufresne, F. and Gerber, H.U. (1988). The surplus immediately before and at ruin, and the amount of the claim causing ruin. Insurance: Mathematics and Economics 7, 193–199.Google Scholar
Gerber, H.U. (1979). An Introduction to Mathematical Risk Theory. Monograph No. 8, S.S. Huebner Foundation, Distributed by R. Irwin, Homewood, IL.Google Scholar
Gerber, H.U. (1988). Mathematical fun with the compound binomial process. Astin Bulletin 18, 161–168.CrossRefGoogle Scholar
Gerber, H.U. and Shiu, E.S.W. (1997). The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance: Mathematics and Economics 21, 129–137.Google Scholar
Gerber, H.U. and Shiu, E.S.W. (1998). On the time value of ruin. North American Actuarial Journal 2, 48–78.CrossRefGoogle Scholar
Grandell, J. (1991). Aspects of Risk Theory. Springer Series in Statistics.CrossRefGoogle Scholar
Janssen, J. (1970). Sur une généralisation du concept de promenade aléatoire sur la droite réelle. Ann. Ins. H. Poincaré, B VI, 249–269.Google Scholar
Janssen, J. and Reinhard, J.M. (1985). Probabilités de ruine pour une classe de modèles de risque semi-Markoviens. Astin Bulletin 15, 123–133.CrossRefGoogle Scholar
Klugman, A.S., Panjer, H.H. and Wilmot, G.E. (1998). Loss Models: From Data to Decisions. Wiley Series in Probability and Statistics.Google Scholar
Newbould, M. (1973). A classification of a random walk defined on a finite Markov chain. Z. Wahrscheinlichkeitstheorie verw. Geh. 26, 95–104.CrossRefGoogle Scholar
Panjer, H.H. and Wang, S. (1993). On the stability of recursive formulas. Astin Bulletin 23, 227–258.CrossRefGoogle Scholar
Reinhard, J.M. (1984). On a class of semi-Markov risk models obtained as classical risk models in a Markovian environment. Astin Bulletin 14, 23–43.CrossRefGoogle Scholar
Reinhard, J.M. and Snoussi, M. (1998). The severity of ruin in a discrete semi Markov risk model. Technical Report 94, ISRO, Université Libre de Bruxelles.Google Scholar
Reinhard, J.M. and Snoussi, M. (2000). The probability of ruin in a discrete semi Markov risk model. To appear in Blätter Deutsche Gesellschaft für Versicherungsmathematik.Google Scholar
Snoussi, M. (1998). The severity of ruin in the Markov-Modulated risk models. Proceedings of the 2nd International Symposium on Semi-Markov Models: Theory and Applications. Ed. by Janssen, J. and Limnios, N., Compiegne, 377–382.Google Scholar
Willmot, G.E. and Lin, X.S. (1998). Exact and approximate properties of the distribution of surplus before and after ruin. Insurance: Mathematics and Economics 23, 91–110.Google Scholar