Gerber-Shiu Theory for Discrete Risk Processes in a Regime Switching Environment

2022/07/12 by Zbigniew Palmowski, Palmowski, Zbigniew, Lewis Ramsden +3 · 1 citation
Business, Management and Accounting · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2207.05339

openalex publication_date 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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) \boldsymbolW_v and \boldsymbolZ_v scale matrices, which were introduced in arXiv:2008.06697. 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.

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