Palmowski, Zbigniew, Ramsden, Lewis and Papaioannou, Apostolos (2024) Gerber-Shiu theory for discrete risk processes in a regime switching environment. Applied Mathematics and Computation. 128491. ISSN 0096-3003
Abstract
In this paper we develop the Gerber-Shiu theory for the classic and dual discrete risk processes in a Markovian (regime switching) environment. In particular, by expressing the Gerber-Shiu function in terms of potential measures of an upward (downward) skip-free discrete-time and discrete-space Markov Additive Process (MAP), we derive closed form expressions for the Gerber-Shiu function in terms of the so-called (discrete) $\bold{W}_v$ and $\bold{Z}_v$ scale matrices, which were introduced in [27]. We show that the discrete scale matrices allow for a unified approach for identifying the Gerber-Shiu function as well as the value function of the associated constant dividend barrier problems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Author(s). |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Social Sciences (York) > The York Management School |
Depositing User: | Pure (York) |
Date Deposited: | 19 Dec 2023 14:40 |
Last Modified: | 16 Oct 2024 19:40 |
Published Version: | https://doi.org/10.1016/j.amc.2023.128491 |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1016/j.amc.2023.128491 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206800 |
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