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Dividend payments in a jump-diffusion risk model with interest and constant dividend barrier. (English) Zbl 1240.91041
Summary: This article considers the compound Poisson insurance risk model perturbed by diffusion with investment and constant dividend barrier. Integro-differential equations for the higher order moments of the discounted dividend payments prior to ruin are derived. Closed-form solutions are formulated when the individual claim amount distribution is exponential. Some satisfying results about the distribution of the aggregate dividend are obtained even for general claim size distributions. We also investigate the number and the amount of the dividend streams. Both the time of ruin and the deficit at ruin are considered in some special cases. Confluent hypergeometric functions play a key role in this paper.
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics