Laplace Transforms Of The Last Exit Times Of Spectrally Negative Levy Processes's Positive Axis

The last exit time is of great significance to the study of getting rid of the negative surplus or total bankruptcy in the risk model.In this paper,we consider Laplace transforms of the last exit time of spectrally negative Lévy processes's positive axis.The last exit time of spectrally negative Lévy processes's positive axis is closely related to the problem of complete bankruptcy.The first passage time is a stopping time,but the last exit time is an non-stopping time.To overcome this difficulties,we use the Poisson method of Li.Yin and Zhou(2017),select a certain eventr,use the first passage time of the certain event to approximate the last exit time,then take limits to reach the required result.The innovation of this paper is to extend the joint Laplace transforms of Li,Yin and Zhou(2017)of the last exit time in a finite exponential time region to the Laplace transforms of non-exponential time.This paper is divided into three chapters.The first chapter introduces the research background and status of the first passage time,occupation time and last exit time of spectrally negative Lévy process;together with a brief introduction of the main results in this thesis.In the second chapter,the first result calculate the Laplace transforms for spec-trally negative Lévy process of the last exit time T0-and the first passage time ?a+.This-paper obtain the Laplace transform at the last exit time of the positive half axis in the case of final bankruptcy before reaching above a and the Laplace transform of the first passage time of a when it has reached above a before the final bankruptcy.The second result obtain the joint Laplace transform at the last exit time of the positive half axis,which generalize the above case of final ruin before reaching above a.In the third chapter,we calculate the Laplace transforms for spectrally negative Lévy process of the last exit time T0-and ?-a-.This paper obtain the first passage time Laplace transform of-a when it has reach below-a before the final bankruptcy and the last exit time Laplace transform when the final ruin does not reach below-a.