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Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion
Authors:Ning Wan  
Affiliation:aDepartment of Applied Mathematics, Tongji University, Shanghai 200092, China
Abstract:In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process perturbed by diffusion. Dividends are paid at a constant rate whenever the modified surplus is above the threshold, otherwise no dividends are paid. Two integro-differential equations for the expected discounted dividend payments prior to ruin are derived and closed-form solutions are given. Accordingly, the Gerber–Shiu expected discounted penalty function and some ruin related functionals, the probability of ultimate ruin, the time of ruin and the surplus before ruin and the deficit at ruin, are considered and their analytic expressions are given by general solution formulas. Finally the moment-generating function of the total discounted dividends until ruin is discussed.
Keywords:Compound Poisson model   Diffusion   Threshold strategy   Dividend payments   Gerber–  Shiu discounted penalty function   Ruin related functionals
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