谱负Lévy过程的最大回撤与最大回升的联合定律

中文摘要 AI 辅助

设X为谱负Lévy过程，其在参数为γ>0的独立指数时间T处被观测。我们研究X在区间[0,T]上的最大回撤与最大回升的联合定律。根据路径的下确界与上确界的两种可能顺序对路径进行分解，在给定这些极值的值及其顺序的条件下，得到的前、中间和后分量相互独立。我们将这些分量的定律确定为被杀死的谱负Lévy过程的Doob h变换，并根据γ尺度函数W(γ)和Z(γ)及其导数明确表达对应的分布函数。将条件定律与极值的联合密度相结合，得到联合分布和矩的积分表示式。

英文摘要

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.

发表机构

• Middle East Technical University（中东理工大学）
• Tubitak SAGE（土耳其国家工程与自然科学研究基金会）

机构由 AI 辅助整理，请以论文原文为准。