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Rate modulation in dams and ruin problems

Part of:Markov processesApplicationsSpecial processes

Published online by Cambridge University Press:  14 July 2016

Søren Asmussen and
Offer Kella
Søren Asmussen*
Affiliation:
University of Lund
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
*
∗ Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-22100 Lund, Sweden.
∗∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel.
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Abstract

We consider a dam in which the release rate depends both on the state and some modulating process. Conditions for the existence of a limiting distribution are established in terms of an associated risk process. The case where the release rate is a product of the state and the modulating process is given special attention, and in particular explicit formulas are obtained for a finite state space Markov modulation.

Keywords

DAMSTORAGE MODELSUBORDINATORLEVY PROCESSRUIN PROBABILITYRISK THEORYSTABILITYSTOCHASTIC INTEREST

MSC classification

Primary:60J27: Continuous-time Markov processes on discrete state spaces62P05: Applications to actuarial sciences and financial mathematics60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996, pp. 523 - 535
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Supported in part by grant 372/93–1 from The Israel Science Foundation.

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