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

被引：0

作者：

Palmowski, Zbigniew ^{[1
]}

Ramsden, Lewis ^{[2
]}

Papaioannouc, Apostolos D. ^{[3
]}

机构：

[1] Wroclaw Univ Sci & Technol, Dept Appl Math, Wroclaw, Poland

[2] Univ York, Sch Business & Soc, York YO10 5DD, Yorks, England

[3] Univ Liverpool, Inst Financial & Actuarial Math, Dept Math Sci, Liverpool L69 7ZL, England

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2024年 / 467卷

关键词：

Gerber-Shiu; Discrete-time; Dual risk process; Markov additive process; Scale matrices; Exit problems; Dividends; Markov-modulation; MARKOV ADDITIVE PROCESSES; DISCOUNTED PENALTY-FUNCTION; POTENTIAL MEASURES; RUIN; PROBABILITIES; MODEL; TIME;

D O I：

10.1016/j.amc.2023.128491

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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) W-v and 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.

引用

页数：14

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