Gerber-Shiu theory for discrete risk processes in a regime switching environment

Zbigniew Palmowski; Lewis Ramsden; Apostolos  Papaioannou

doi:10.1016/j.amc.2023.128491

Gerber-Shiu theory for discrete risk processes in a regime switching environment

Zbigniew Palmowski, Lewis Ramsden, Apostolos Papaioannou

The York Management School

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

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.

Original language	English
Article number	128491
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	467
Early online date	11 Dec 2023
DOIs	https://doi.org/10.1016/j.amc.2023.128491
Publication status	Published - 15 Apr 2024

Bibliographical note

Access to Document

10.1016/j.amc.2023.128491Licence: CC BY-NC-ND

1-s2.0-S0096300323006604-main
© 2023 The Author(s). Published by Elsevier Inc
Final published version, 643 KBLicence: CC BY-NC-ND

Cite this

@article{a620559a27ba49589cbfe2fc2e3ea1c3,

title = "Gerber-Shiu theory for discrete risk processes in a regime switching environment",

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.",

author = "Zbigniew Palmowski and Lewis Ramsden and Apostolos Papaioannou",

note = "{\textcopyright} 2023 The Author(s).",

year = "2024",

month = apr,

day = "15",

doi = "10.1016/j.amc.2023.128491",

language = "English",

volume = "467",

journal = "Applied Mathematics and Computation ",

issn = "0096-3003",

publisher = "Elsevier",

}

TY - JOUR

T1 - Gerber-Shiu theory for discrete risk processes in a regime switching environment

AU - Palmowski, Zbigniew

AU - Ramsden, Lewis

AU - Papaioannou, Apostolos

PY - 2024/4/15

Y1 - 2024/4/15

N2 - 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.

AB - 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.

U2 - 10.1016/j.amc.2023.128491

DO - 10.1016/j.amc.2023.128491

M3 - Article

SN - 0096-3003

VL - 467

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 128491

ER -