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Optimal dividends in a risk model with dependence between claim sizes and claim intervals

In this paper, we investigate the optimal dividends in a classical surplus process with a dependence structure between the claim sizes and the interarrival times. We first obtain an integro-differential equation satisfied by the discounted dividend payments. Then we derive the explicit expression of the discounted dividend payments for exponential claims. Furthermore, we discuss the optimal dividend barrier when the claim sizes have a common exponential distribution. Finally, we give the numerical examples for exponential claims.