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

Zbigniew Palmowski, Lewis Ramsden and Apostolos D. Papaioannou

Applied Mathematics and Computation, 2024, vol. 467, issue C

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.

Keywords: Gerber-Shiu; Discrete-time; Dual risk process; Markov additive process; Scale matrices; Exit problems; Dividends; Markov-modulation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:467:y:2024:i:c:s0096300323006604

DOI: 10.1016/j.amc.2023.128491

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