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Zbl 1163.91438
Lu, Yi; Li, Shuanming
The Markovian regime-switching risk model with a threshold dividend strategy. (English)
[J] Insur. Math. Econ. 44, No. 2, 296-303 (2009). ISSN 0167-6687

Summary: We study a regime-switching risk model with a threshold dividend strategy, in which the rate for the Poisson claim arrivals and the distribution of the claim amounts are driven by an underlying (external) Markov jump process. The purpose of this paper is to study the unified Gerber-Shiu discounted penalty function and the moments of the total dividend payments until ruin. We adopt an approach which is akin to the one used by {\it X. Lin} und {\it K. P. Pavlova} [Insur. Math. Econ. 38, No. 1, 57--80 (2006; Zbl 1157.91383)] to extend the results for the classical risk model with a threshold dividend strategy to our model. The matrix form of systems of integro-differential equations is presented and the analytical solutions to these systems are derived. Finally, numerical illustrations with exponential claim amounts are also given.

MSC 2000:: *91B30 Risk theory etc.
91B28 Finance etc.

Keywords: Gerber-Shiu function; integro-differential equation; present value of dividend payments; regime-switching model; threshold dividend strategy

Citations: Zbl 1157.91383

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