The Poisson Approach Of Occupation Time For Spectrally Negative Lévy Process And Related Issues

The study Spectrally negative process is a hot spot of stochastic process research in recent years as a process,with independent stationary increment and no positive jump-s.The Laplace transform of occupation times are associated with the ruin probability of the risk theory and are increasingly used in risk models,option pricing and Omega risk models.Many scholars have used different approaches to obtain the Laplace trans-form of the Spectrally negative Lévy process.This paper further studies the Poisson approach.This paper is divided into four chapters.The first chapter introduces the related research background as well as the present development in this field at home and abroad,and then briefly describes the main research results of this paper.In the second chapter,using the Poisson approach we find Laplace transforms of occupation times of intervals until first passage times for spectrally negative Lévy processes,The final explicit expression is consistent with the conclusion of Loeffen et al.(2014).In the third chapter,we study Laplace transforms of joint occupation times over n disjoint intervals until first passage times.For spectrally negative Lévy processes and 0 = a0?a1?…?an,?0,?1…,?n-1?0?0?x?an,Expressions such as(?)Laplace transforms of joint occupation times and the Poisson approach is used to obtain the explicit expression.In the fourth chapter,based on the conclusion of Loeffen et al.(2014),we use change of measures to study joint occupation times with Parameter X?0-.Expressions such as(?)The results are expressed by the corresponding scale functions...