Rate modulation in dams and ruin problems

Søren Asmussen; Offer Kella

doi:10.1017/S0021900200099940

Rate modulation in dams and ruin problems

Søren Asmussen^*
, Offer Kella

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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.

Original language	English
Pages (from-to)	523-535
Number of pages	13
Journal	Journal of Applied Probability
Volume	33
Issue number	2
DOIs	https://doi.org/10.1017/S0021900200099940
State	Published - Jun 1996

Keywords

Dam
Lévy process
Risk theory
Ruin probability
Stability
Stochastic interest
Storage model
Subordinator

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10.1017/S0021900200099940

Cite this

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title = "Rate modulation in dams and ruin problems",

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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AB - 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.

KW - Dam

KW - Lévy process

KW - Risk theory

KW - Ruin probability

KW - Stability

KW - Stochastic interest

KW - Storage model

KW - Subordinator

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ER -

Rate modulation in dams and ruin problems

Abstract

Keywords

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