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Zbl 1153.91608
Zhang, Xin
On the ruin problem in a Markov-modulated risk model. (English)
[J] Methodol. Comput. Appl. Probab. 10, No. 2, 225-238 (2008). ISSN 1387-5841; ISSN 1573-7713/e

Summary: In this paper, we consider the compound Poisson risk model influenced by an external Markovian environment process, i.e. Markov-modulated compound Poisson model. The explicit Laplace transforms of Gerber-Shiu functions are obtained, while the explicit Gerber-Shiu functions are derived for the $K_{n}$-family claim size distributions in the two-states case.

MSC 2000:: *91B30 Risk theory etc.

Keywords: Markov additive process; Laplace transform; Gerber-Shiu function; Markov-modulated compound Poisson model

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Zentralblatt MATH Berlin [Germany]