把开始于u(u≥0)的谱负Levy过程看作是推广的风险模型,得出了用Wδ(x)表达的 e^(-δt)gt(x)dt(gt(x)被看作是过程在时刻t的密度函数)与推广的Dickson公式。此外还对特殊情况下的尺度函数Wδ(x)给出了确切的表达式。
Regarding the spectrally negative Levy process starting at u(u≥0) as the generalized risk model, the paper derives the explicit expression for integral from n=0 to∞e^(-δt)gt(x)dt(gt(x) is supposed to be the density function of the process at time t) with the scale function Wδ(x).Futher the generalized Dickson's formula are proposed.In addition, the explicit expression for the scale function Wδ(x) in special cases is given.