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

Zbigniew Palmowski, Lewis Ramsden, Apostolos Papaioannou

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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 languageEnglish
Article number128491
Number of pages14
JournalApplied Mathematics and Computation
Early online date11 Dec 2023
Publication statusPublished - 15 Apr 2024

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