Year: 2026
Type: preprint
Abstract: Let X be a spectrally negative Lévy process observed up to an inde- pendent exponential time T with parameter γ > 0. We study the joint law of the maximum drawdown and the maximum drawup of X on [0, T ]. The path is decomposed according to the two possible orderings of its in- fimum and supremum. Conditional on the values of these extrema and on their ordering, the resulting pre-, intermediate, and post- components are independent. We identify their laws as Doob h-transforms of killed spec- trally negative Lévy processes and express the corresponding distribution functions explicitly in terms of the γ-scale functions W (γ) and Z(γ) and their derivatives. Combining the conditional laws with the joint densities of the extrema yields integral representations of the joint distribution and moments.
Source: arXiv (Cornell University)
Authors: Acar, Ceren Vardar, Akdogan, Emre
Institution: Türkiye Bilimsel ve Teknolojik Araştırma Kurumu
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7208788585