The Joint Laplace Transforms For Spectrally Negative Lévy Processes With The Value Of The Process

The first passage time is the first time that passage a certain level for a stochatic process,it is an important issue in risk models.As well as,the last exit time is the time that leave a certain leval for a stochatic process,which can be regarded as the final recovery normal time that after no longer bankrupt or the time of final ruin,it has attracted extensive attention of scholars at home and abroad.This paper is to study the joint Laplace transforms for spectrally negative Levy processes about the first passage time,or the last exit time with the value of the process.There are four chapters in this paper,as follows:In chapter 1,we introduce the research background and current situation of the first passage time and the last exit time in spectrally negative Levy processes,and list of the main research contents.In chapter 2,we explain that spectrally negative Levy processes,scale functions,some fluctuation identities and principle of perturbation approach.In chapter 3,we calculate the joint Laplace transforms about the time T0+ related to the final recovery normal time that after no longer bankrupt for spectrally negative Levy processes,such asIn chapter 4,we calculate the joint Laplace transforms about the time T0-related to the time of final ruin for spectrally negative Levy processes,such as In this paper,we have?0+=sup{t?0:Xt<0},T0-=sup{t?0:Xt>0},?-a-=inf{t>0:Xt<-a},?a+=inf{t>0:Xt>a?,with the convention sup (?)=0,inf (?)=?).