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 X. Lin
und 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.