Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints

DOI10.1137/15M1025256zbMath1351.60048arXiv1506.04063OpenAlexW2963644125MaRDI QIDQ2818217

Xiaolu Tan, Nizar Touzi, Gaoyue Guo

Publication date: 6 September 2016

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Abstract: The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod embedding problem to the case of finitely-many marginal constraints. Using the classical convex duality approach together with the optimal stopping theory, we obtain the duality results which are formulated by means of probability measures on an enlarged space. We also relate these results to the problem of martingale optimal transport under multiple marginal constraints.

Full work available at URL: https://arxiv.org/abs/1506.04063

zbMATH Keywords

Brownian motionstopping timeconvex dualityrobust hedgingSkorokhod embeddingmartingale optimal transportmodel-free pricing

Mathematics Subject Classification ID

Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20) Duality theory (optimization) (49N15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The maximum maximum of a martingale with given \(n\) marginals
• On a problem of optimal transport under marginal martingale constraints
• Model-independent bounds for option prices -- a mass transport approach
• A model-free no-arbitrage price bound for variance options
• Optimal transportation under controlled stochastic dynamics
• Martingale optimal transport and robust hedging in continuous time
• Robust pricing and hedging of double no-touch options
• Robust price bounds for the forward starting straddle
• Martingale optimal transport in the Skorokhod space
• Tightness and duality of martingale transport on the Skorokhod space
• Optimal multiple stopping time problem
• An explicit martingale version of the one-dimensional Brenier's theorem with full marginals constraint
• Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping
• The Skorokhod embedding problem and its offspring
• Robust hedging of the lookback option
• Some results on Skorokhod embedding and robust hedging with local time
• Robust pricing-hedging dualities in continuous time
• Complete duality for martingale optimal transport on the line
• The minimum maximum of a continuous martingale with given initial and terminal laws
• On pathwise stochastic integration
• Optimal Skorokhod embedding given full marginals and Azéma-Yor peacocks
• Optimal transport and Skorokhod embedding
• An iterated Azéma-Yor type embedding for finitely many marginals
• A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
• Skorokhod embeddings, minimality and non-centred target distributions
• Markov-Komposition und eine Anwendung auf Martingale. (Markov compositions and an application to martingales)
• Robust Hedging of Barrier Options
• A Pseudo-Markov Property for Controlled Diffusion Processes
• On the Monotonicity Principle of Optimal Skorokhod Embedding Problem
• ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS
• The Skorokhod Embedding Problem and Model-Independent Bounds for Option Prices
• ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES
• [https://portal.mardi4nfdi.de/wiki/Publication:5646185 Th�orie des processus stochastiques g�n�raux applications aux surmartingales]
• On Embedding Right Continuous Martingales in Brownian Motion
• Optimal Transport
• The maximum maximum of a martingale constrained by an intermediate law

Related Items (19)

Fine properties of the optimal Skorokhod embedding problem ⋮ Canonical supermartingale couplings ⋮ Some results on Skorokhod embedding and robust hedging with local time ⋮ A dynamic programming approach to distribution-constrained optimal stopping ⋮ Martingale optimal transport duality ⋮ Pathwise superreplication via Vovk's outer measure ⋮ Perturbation analysis of sub/super hedging problems ⋮ Geometry of vectorial martingale optimal transportations and duality ⋮ Supermartingale Brenier's theorem with full-marginals constraint ⋮ On the Root Solution to the Skorokhod Embedding Problem Given Full Marginals ⋮ Optimal Brownian Stopping When the Source and Target Are Radially Symmetric Distributions ⋮ Pathwise superhedging for time-dependent barrier options on càdlàg paths -- finite or infinite tradeable European, one-touch, lookback or forward starting options ⋮ Optimal martingale transport between radially symmetric marginals in general dimensions ⋮ A free boundary characterisation of the root barrier for Markov processes ⋮ An explicit martingale version of the one-dimensional Brenier's theorem with full marginals constraint ⋮ Multiperiod martingale transport ⋮ On the Monotonicity Principle of Optimal Skorokhod Embedding Problem ⋮ Model-independent pricing with insider information: a skorokhod embedding approach ⋮ Optimal transport and Skorokhod embedding

This page was built for publication: Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints