On the monotonicity principle of optimal Skorokhod embedding problem

Gaoyue Guo; Xiaolu Tan; Nizar Touzi

doi:10.1137/15M1025268

On the monotonicity principle of optimal Skorokhod embedding problem

Gaoyue Guo, Xiaolu Tan, Nizar Touzi

Finance and Risk Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

This is a continuation of our accompanying paper [SIAM J. Control Optim., 54 (2016), pp. 2174-2201] We provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established in [Beiglböck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013]. Our proof is based on the adaptation of the Monge-Kantorovich duality in our context, a delicate application of the optional cross-section theorem, and a clever conditioning argument introduced in [Beiglböck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013].

Original language	English (US)
Pages (from-to)	2478-2489
Number of pages	12
Journal	SIAM Journal on Control and Optimization
Volume	54
Issue number	5
DOIs	https://doi.org/10.1137/15M1025268
State	Published - 2016

Keywords

Monotonicity principle
Optimal Skorokhod embedding
Stop-go pair

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1137/15M1025268

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title = "On the monotonicity principle of optimal Skorokhod embedding problem",

abstract = "This is a continuation of our accompanying paper [SIAM J. Control Optim., 54 (2016), pp. 2174-2201] We provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established in [Beiglb{\"o}ck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013]. Our proof is based on the adaptation of the Monge-Kantorovich duality in our context, a delicate application of the optional cross-section theorem, and a clever conditioning argument introduced in [Beiglb{\"o}ck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013].",

keywords = "Monotonicity principle, Optimal Skorokhod embedding, Stop-go pair",

author = "Gaoyue Guo and Xiaolu Tan and Nizar Touzi",

note = "Funding Information: This work received financial support from ERC 321111 Rofirm, ANR Isotace, Chairs Financial Risks (Risk Foundation, sponsored by Soci{\'e}t{\'e} G{\'e}n{\'e}rale), and Finance and Sustainable Development (IEF sponsored by EDF and CA). We are grateful to two anonymous referees for their helpful suggestions. Publisher Copyright: {\textcopyright} 2016 Society for Industrial and Applied Mathematics.",

year = "2016",

doi = "10.1137/15M1025268",

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T1 - On the monotonicity principle of optimal Skorokhod embedding problem

AU - Guo, Gaoyue

AU - Tan, Xiaolu

AU - Touzi, Nizar

N1 - Funding Information: This work received financial support from ERC 321111 Rofirm, ANR Isotace, Chairs Financial Risks (Risk Foundation, sponsored by Société Générale), and Finance and Sustainable Development (IEF sponsored by EDF and CA). We are grateful to two anonymous referees for their helpful suggestions. Publisher Copyright: © 2016 Society for Industrial and Applied Mathematics.

PY - 2016

Y1 - 2016

N2 - This is a continuation of our accompanying paper [SIAM J. Control Optim., 54 (2016), pp. 2174-2201] We provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established in [Beiglböck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013]. Our proof is based on the adaptation of the Monge-Kantorovich duality in our context, a delicate application of the optional cross-section theorem, and a clever conditioning argument introduced in [Beiglböck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013].

AB - This is a continuation of our accompanying paper [SIAM J. Control Optim., 54 (2016), pp. 2174-2201] We provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established in [Beiglböck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013]. Our proof is based on the adaptation of the Monge-Kantorovich duality in our context, a delicate application of the optional cross-section theorem, and a clever conditioning argument introduced in [Beiglböck, Cox, and Huesmann, Optimal Transport and Skorokhod Embedding, preprint, 2013].

KW - Monotonicity principle

KW - Optimal Skorokhod embedding

KW - Stop-go pair

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On the monotonicity principle of optimal Skorokhod embedding problem

Abstract

Keywords

ASJC Scopus subject areas

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