Occupation times of intervals until last passage times for spectrally   negative Levy processes
  In this paper, we derive the joint Laplace transforms of occupation times until its last passage times as well as its positions. Motivated by Baurdoux [2], the last times before an independent exponential variable are studied. By applying dual arguments, explicit formulas are derived in terms of new analytical identities from Loeffen et al. [12]. 
Bo Li, Chunhao Cai
math.PR