RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Theory Stoch. Process.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Theory Stoch. Process., 2017, Volume 22(38), Issue 1, Pages 30–40 (Mi thsp169)  

Maximization of functionals depending on the terminal value and the running maximum of a martingale: a mass transport approach

Nikolay Lysenko

National Research University Higher School of Economics, Faculty of Mathematics, 119048 Moscow, Usacheva str., 6

Abstract: It is known that the Azéma-Yor solution to the Skorokhod embedding problem maximizes the law of the running maximum of a uniformly integrable martingale with a given terminal value distribution. Recently this optimality property has been generalized to expectations of certain bivariate cost functions depending on the terminal value and the running maximum. In this paper we give an extension of this result to another class of functions. In particular, we study a class of cost functions for which the corresponding optimal embeddings are not Azéma-Yor. The suggested approach is quite straightforward modulo basic facts of the Monge-Kantorovich mass transportation theory. Loosely speaking, the joint distribution of the running maximum and the terminal value in the Azéma-Yor embedding is concentrated on the graph of a monotone function, and we show that this fact follows from the cyclical monotonicity criterion for solutions to the Monge-Kantorovich problem.

Keywords: Skorokhod problem, Azéma-Yor embedding, Monge-Kantorovich problem, optimal transport, supermodular functions, running maximum and the terminal value of a martingale.

Funding Agency Grant Number
National Research University Higher School of Economics 14-05-0007
The article was prepared within the framework of the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2014–2015 (grant 14-05-0007) and supported within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.


Full text: PDF file (265 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 60G44
Language:

Citation: Nikolay Lysenko, “Maximization of functionals depending on the terminal value and the running maximum of a martingale: a mass transport approach”, Theory Stoch. Process., 22(38):1 (2017), 30–40

Citation in format AMSBIB
\Bibitem{Lys17}
\by Nikolay Lysenko
\paper Maximization of functionals depending on the terminal value and the running maximum of a martingale: a mass transport approach
\jour Theory Stoch. Process.
\yr 2017
\vol 22(38)
\issue 1
\pages 30--40
\mathnet{http://mi.mathnet.ru/thsp169}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3742387}
\zmath{https://zbmath.org/?q=an:1399.60073}


Linking options:
  • http://mi.mathnet.ru/eng/thsp169
  • http://mi.mathnet.ru/eng/thsp/v22/i1/p30

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Theory of Stochastic Processes
    Number of views:
    This page:60
    Full text:10
    References:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019