کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1155401 958722 2016 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint
ترجمه فارسی عنوان
نسخه مارتینگیل صریح و روشن از قضیه Brenier تک بعدی با محدودیت کامل حاشیه ای
کلمات کلیدی
حمل و نقل مارتینگیل مطلوب، قضیه Brenier . PCOC؛ حرکت براونی جعلی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

We provide an extension of the martingale version of the Fréchet–Hoeffding coupling to the infinitely-many marginals constraints setting. In the two-marginal context, this extension was obtained by Beiglböck and Juillet (2016), and further developed by Henry-Labordère and Touzi (in press), see also Beiglböck and Henry-Labordère (Preprint).Our main result applies to a special class of reward functions and requires some restrictions on the marginal distributions. We show that the optimal martingale transference plan is induced by a pure downward jump local Lévy model. In particular, this provides a new martingale peacock process (PCOC “Processus Croissant pour l’Ordre Convexe,” see Hirsch et al. (2011), and a new remarkable example of discontinuous fake Brownian motions. Further, as in Henry-Labordère and Touzi (in press), we also provide a duality result together with the corresponding dual optimizer in explicit form.As an application to financial mathematics, our results give the model-independent optimal lower and upper bounds for variance swaps.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 126, Issue 9, September 2016, Pages 2800–2834
نویسندگان
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