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Moments analysis of a Markov-modulated risk model with stochastic interest rates

Abstract. In this paper we determine explicitly the closed form of the moments of a Markov-Modulated Risk Model with Stochastic Interest Rate. The moments are derived by means of Laplace-Stieltjes transforms. Equations and formulas are conveniently represented by using the 2-dimensional matrix formalism. This paper substantially extends the results of Kim and Kim (Insurance: Mathematics and Economics 40, 485-497, 2007) by allowing the possibility to work with a stochastic modulated interest rate and by considering a company having several business lines. A numerical example is provided to show possible applications of the model.