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

Palmowski, Zbigniew, Ramsden, Lewis and Papaioannou, Apostolos D (2024) Gerber-Shiu theory for discrete risk processes in a regime switching environment. Applied Mathematics and Computation, 467. p. 128491.

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Official URL: http://dx.doi.org/10.1016/j.amc.2023.128491

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) Wv and Zv 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.

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	20 Dec 2023 15:44
Last Modified:	18 Apr 2024 09:00
DOI:	10.1016/j.amc.2023.128491
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3177562