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This paper concerns the numerical solution of the expected discounted dividend payments in a Markov-modulated risk model with investment, transaction costs and threshold dividend strategy. A system of delay integro-differential equations with certain boundary conditions is derived. As a closed-form solution does not exist, a numerical sinc method is proposed. Furthermore, an example is considered to illustrate the effect of the transaction costs, investment strategy and market environment.

A markov-modulated risk model with transaction costs and threshold dividend strategy