We consider the spectrally negative Levy processes and determine the joint
laws for the quantities such as the first and last passage times over a fixed
level, the overshoots and undershoots at first passage, the minimum, the
maximum and the duration of negative values. We apply our results to insurance
risk theory to find an explicit expression for the generalized expected
discounted penalty function in terms of scale functions. Further, a new
expression for the generalized Dickson's formula is provided.Comment: To appear in Front. Math. Chin
