谱负Levy过程的三者联合密度函数与Gerber-Shiu折现罚金函数(英文)

The joint density function of three characteristics and the Gerber-Shiu discounted penalty function for the spectrally negative Levy process

将开始于u(≥0)的谱负Levy过程(即没有正跳的Levy过程)看作推广的风险模型,得到了破产时刻和破产瞬间前后余额三者的联合密度函数,运用已得结论和∫∞e-δtgt(x)dt(gt(x)为过程在时刻t的密度函数)给出了Gerber-Shiu折现罚金函数.

The spectrally negative Levy process starting at u（≥0） （namely the Levy process with no positive jumps） is regarded as the generalized risk model and the joint density function of three characteristics： the time of ruin, the surpluses immediately before and at ruin is obtained. Using the derived results and ∫0^∞ e^-a gt （x）dt where g, （x） is supposed to be the density function of the process at time t, the Gerber-Shiu discounted penalty function for the spectrally negative Levy process is proposed.