The Problem Of Share Out Bonus Of The Dual Risk Model Research

Insurance risk model is issued out first by De.Finetti.Since then, many scholarsresearch on it foundly. This paper is focus on dividend issue of dual risk model. Firstly, thepaper introduced dividend function and the integral function briefly, especially for theEquations of dividends-Differential Equations; Secondly, on the dimensional perturbedrisk model with or without stochastic disturbalance, which includes the discountedexpected function about the dual risk model with three dividend rate and the ruinprobability on the bidimensional perturb risk model. Thirdly, Adual model of the perturbedclassical compound poission risk model under a constant dividend barrier was considered.A new method is used in deriving the boundary condition of the equation satisfied by thatexpectation on function by using the local time of a related process. The Expression for theexpected discounted dividend function was obtained in terms of those in the correspondingperturbed compound Poisson risk model without barrier. The special cases where the gainsize is phase-type distribute disillustrated in the last section. At last the existence of theoptimal dividend level was considered.