The maximum surplus before ruin and related problems in a jump-diffusion renewal risk process |
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Authors: | Shan Shan Wang Chun Sheng Zhang |
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Institution: | [1]Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China [2]School of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China |
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Abstract: | In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly
study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity
is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous
integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg’s equation,
the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long
as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted
dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results. |
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Keywords: | Sparre Andersen risk model phase-type inter-claim times maximum surplus before ruin expected present value of dividends barrier dividend strategy diffusion integro-differential equation |
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