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Rate modulation in dams and ruin problems

Part of: Applications Markov processes Special 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 spaces 62P05: Applications to actuarial sciences and financial mathematics 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
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.

References

[1] Asmussen, S. (1996) Ruin Probabilities. World Scientific, Singapore.Google Scholar
[2] Asmussen, S. and Schock Petersen, S. (1989) Ruin probabilities expressed in terms of storage processes. Adv. Appl Prob. 20, 913–916.CrossRefGoogle Scholar
[3] Brockwell, P. J., Resnick, S. I. and Tweedie, R. L. (1982) Storage processes with general release rule and additive inputs. Adv. Appl. Prob. 14, 392–433.Google Scholar
[4] Clifford, P. and Sudbury, A. (1985) A sample path proof of the duality for stochastically monotone Markov processes. Ann. Prob. 13, 558–565.CrossRefGoogle Scholar
[5] Embrechts, P., Jensen, J. L., Maejima, M. and Teugels, J. L. (1985) Approximations for compound Poisson and Polya processes. Adv. Appl. Prob. 17, 623–637.Google Scholar
[6] Franken, P., König, D., Arndt, U. and Schmidt, V. (1982) Queues and Point Processes. Wiley, New York.Google Scholar
[7] Harrison, J. M. (1977) Ruin problems with compounding assets. Stock Proc. Appl. 5, 67–79.CrossRefGoogle Scholar
[8] Harrison, J. M. and Resnick, S. I. (1977) The recurrence classification of risk and storage processes. Math. Operat. Res. 3, 57–66.Google Scholar
[9] Kaspi, H. (1984) Storage processes with Markov additive input and output. Math. Operat. Res. 9, 424–440.Google Scholar
[10] Prabhu, N. U. (1980) Stochastic Storage Processes. Queues, Insurance Risk, and Dams. Springer, New York.Google Scholar
[11] Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
[12] Siegmund, D. (1976) The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes. Ann. Prob. 4, 914–924.Google Scholar
[13] Sigman, K. (1989) One-dependent regenerative processes and queues in continuous time. Math. Operat. Res. 15, 175–189.Google Scholar
[14] Sundt, B. (1991) An Introduction to Non-Life Insurance Mathematics. Versicherungswirtschaft, Karlsruhe.Google Scholar