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We consider the Sparre Andersen model modified by the inclusion of interest on the surplus.Approximation for the ultimate ruin probability is derived by rounding.And upper bound and lower bound arealso derived by rounding-down and rounding-up respectively.According to the upper bound and lower bound,we can easily obtain the error estimation of the approximation.Applications of the results to the compoundPoisson model are given.  相似文献
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In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy (even that of the optimal dividend strategy). Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang (2) and compound Poisson risk models are also given.  相似文献
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We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant.The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.  相似文献
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In this paper, we discuss the influence of multiple values and Valiron deficiencies on the uniqueness problem of algebroid functions on annuli, we get the several uniqueness theorems of algebroid functions on annuli, and also we extend the Nevanlinna value distribution theory for algebroid functions on annuli.  相似文献
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In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.  相似文献
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