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Rate modulation in dams and ruin problems
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 1996
Footnotes
Supported in part by grant 372/93–1 from The Israel Science Foundation.
References
[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
[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
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