The Classic Model Dividends Solutions Discussion

This article considers the compound Poisson risk model with threshold dividend strategy. We get the renewal equation for classical risk model and obtain the solution of dividend function under special condition.First, we get the renewal function about the classical risk model with threshold strategy and obtain the ordinary differential equation about V(x, b) under the condition ofwhere pⁱ(x) is the i-th derivation of claim amount probability density function. B_i,i = 1,2,3,…, n are constants. Using the knoweldge of differentional equation, we can solve this ordinary differential equation about V(x,b), and obtain the formula of dividend function. Then, by the sane means we discuss the compound Poisson process perturbed by a diffusion. Finally, we get renewal equation of dividend function about the classical risk model with a diffusion and the solution in particular condition.