Maximum Drawdown and Drawdown Duration of Spectrally Negative Lévy Processes Decomposed at Extremes

Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative Lévy process taken up to an independent exponential time T . As a result, mainly the distributions of the supremum of the post-infimum process and the maximum drawdown of the pre-/post-supremum, post-infimum processes and the intermediate processes are obtained together with the law of drawdown durations.