A1877
Title: Joint distributions of maximum drawdown and maximum drawup for spectrally negative Levy processes
Authors: Ceren Vardar Acar - Middle East Technical University, Turkey, Dumlupinar Bulvari No:1 (Turkey) [presenting]
Abstract: Path-decomposition and scale-function methods are presented for the joint analysis of maximum drawdown and maximum drawup of spectrally negative Levy processes observed up to an independent exponential time. The methodological decomposition of the problem is stated according to the two possible orderings of the infimum and the supremum. The path decompositions are collected at the stopping times of the infimum and the supremum, including the two orderings of these extremal times. These decompositions result in explicit conditional distributions of the maximum drawdowns and maximum drawups of the independent path segments, and the conditional laws are combined with the joint distributions of the extrema to yield the joint distribution of the maximum drawdown and maximum drawup. The final section provides a summary of the contribution and discusses extensions to durations and statistical applications.
