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A Note on Ruin in a Two State Markov Model1

Published online by Cambridge University Press:  29 August 2014

Christian Wagner
Christian Wagner*
Affiliation:
Wagner & Kunz Aktuare AG, Steinenbachgässlein 27, CH-4051 Basel, E-mail:wagner@aktuare.ch
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Abstract

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We are dealing with the ruin probability and the expected ruin time in a two state Markov model where the premium is the reciprocal of an integer and the initial surplus is a multiple of the premium.

Keywords

Markov chainRuin timeRuin probability
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 2 , November 2001 , pp. 349 - 358
Copyright
Copyright © International Actuarial Association 2001

Footnotes

1

The author is indebted to the editor and an anonymous referee for their helpful comments and some simplified derivations of formulae, especially in section 3.

References

Asmussen, S. (2000) Ruin probabilities. Advanced Series on Statistical Science and Applied probability 2, World Scientific, Singapore.Google Scholar
Bäuerle, N. (1996) Some results about the expected ruin time in Markov-modulated risk models. Insurance: Mathematics and Economics 18, 119–127.Google Scholar
Dickson, D.C.M. and Waters, H.R. (1992) The probability and severity of ruin in finite and infinite time. ASTIN Bulletin 22, 177–190.CrossRefGoogle Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications II, 2nd ed., Wiley, New York.Google Scholar
Reinhard, J.M. and Snoussi, M. (2000) The probability of ruin in a discrete semi-Markov risk model. Blätter der Deutschen Gesellschaft für Versicherungsmathematik XXIV, 477–490.Google Scholar
Rolski, T., Schmidli, H., Teugels, J. and Schmidt, V. (1999) Stochastic processes for insurance and finance. Wiley Series in Probability and Statistics, Chichester.CrossRefGoogle Scholar