Occupation Times of Intervals Until Last Passage Times for Spectrally Negative Lévy Processes

Convolution Equivalent Lévy Processes and First Passage Times

We investigate the behavior of Lévy processes with convolution equivalent Lévy measures, up to the time of first passage over a high level u. Such problems arise naturally in the context of insurance risk where u is the initial reserve. We obtain a precise asymptotic estimate on the probability of first passage occurring by time T . This result is then used to study the process conditioned on f...

Processes of Class Sigma, Last Passage Times, and Drawdowns

We propose a general framework for studying last passage times, suprema and drawdowns of a large class of continuous-time stochastic processes. Our approach is based on processes of class Sigma and the more general concept of two processes, one of which moves only when the other is at the origin. After investigating certain transformations of such processes and their convergence properties, we ...

Last Passage times of Minimum Contrast Estimators

Moments of passage times for Lévy processes

We give necessary and sufficient conditions, in terms of characteristics of the process, for finiteness of moments of passage times of general Lévy processes above horizontal, linear or certain curved boundaries. They apply in particular to processes which drift almost surely to infinity, and lead to estimates of the rate of growth of certain expectations, constituting generalised kinds of rene...

Occupation Times of Refracted Lévy Processes

A refracted Lévy process is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More precisely, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation dUt = −δ1{Ut>b}dt + dXt , t ≥ 0 where X = (Xt , t ≥ 0) is a Lévy p...