Monotone martingale transport plans and Skorokhod embedding

Beiglböck, Mathias; Henry-Labordère, Pierre; Touzi, Nizar

doi:10.1016/j.spa.2017.01.004

Cited by 44 publications

(54 citation statements)

References 47 publications

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“…We also refer to the subsequent literature on martingale optimal transport by [6,7,8,14,15,19,20,21,23,25], etc.…”

Section: Introductionmentioning

confidence: 99%

On the Monotonicity Principle of Optimal Skorokhod Embedding Problem

Guo¹,

Tan²,

Touzi³

2016

SIAM J. Control Optim.

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This is a continuation of our accompanying paper [18]. We provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established in Beiglböck, Cox & Huesmann [2]. 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 [2].

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“…We also refer to the subsequent literature on martingale optimal transport by [6,7,8,14,15,19,20,21,23,25], etc.…”

Section: Introductionmentioning

confidence: 99%

On the Monotonicity Principle of Optimal Skorokhod Embedding Problem

Guo¹,

Tan²,

Touzi³

2016

SIAM J. Control Optim.

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“…[9,28,47]). As observed in [5] one can gain insight into the martingale transport problem between two probabilities µ 1 and µ 2 by relating it to a Skorokhod embedding problem which may be considered as continuous time version of the martingale transport problem. Notably this idea can be used to recover the known solutions of the martingale optimal transport problem in a unified fashion ( [39]).…”

Section: • Martingale Optimal Transportmentioning

confidence: 99%

The geometry of multi-marginal Skorokhod Embedding

Beiglböck

Cox

Huesmann

2019

Probab. Theory Relat. Fields

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The Skorokhod Embedding Problem (SEP) is one of the classical problems in the study of stochastic processes, with applications in many different fields (cf. the surveys [48,34]). Many of these applications have natural multi-marginal extensions leading to the (optimal) multi-marginal Skorokhod problem (MSEP). Some of the first papers to consider this problem are [32,10,44]. However, this turns out to be difficult using existing techniques: only recently a complete solution was be obtained in [14] establishing an extension of the Root construction, while other instances are only partially answered or remain wide open.In this paper, we extend the theory developed in [2] to the multi-marginal setup which is comparable to the extension of the optimal transport problem to the multi-marginal optimal transport problem. As for the one-marginal case, this viewpoint turns out to be very powerful. In particular, we are able to show that all classical optimal embeddings have natural multi-marginal counterparts. Notably these different constructions are linked through a joint geometric structure and the classical solutions are recovered as particular cases.Moreover, our results also have consequences for the study of the martingale transport problem as well as the peacock problem.

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“…Henry-Labordère and Touzi [18] extended the results of Beiglböck and Juillet [4] and showed optimality for a wider class of payoff functions. Beiglböck et al [6] analysed the left-curtain coupling further and gave a simplified proof of uniqueness under the additional assumption that µ is continuous. Juillet [27] proved that π lc is continuous, and thus, for general distributions, it can be approximated by the left-curtain couplings corresponding to 'nice' (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…finitely supported or continuous) initial and/or target laws. A number of further articles investigate the properties and extensions of π lc , see Beiglböck et al [3,6], Nutz et al [29,30].…”

Section: Introductionmentioning

confidence: 99%

The left-curtain martingale coupling in the presence of atoms

Hobson¹,

Norgilas²

2019

Ann. Appl. Probab.

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Beiglböck and Juillet [4] introduced the left-curtain martingale coupling of probability measures µ and ν, and proved that, when the initial law µ is continuous, it is supported by the graphs of two functions. We extend the later result by constructing the generalised left-curtain martingale coupling and show that for an arbitrary starting law µ it is characterised by two appropriately defined lower and upper functions.As an application of this result we derive the model-independent upper bound of an American put option. This extends recent results of Hobson and Norgilas [26] on the atom-free case.

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Monotone martingale transport plans and Skorokhod embedding

Cited by 44 publications

References 47 publications

On the Monotonicity Principle of Optimal Skorokhod Embedding Problem

On the Monotonicity Principle of Optimal Skorokhod Embedding Problem

The geometry of multi-marginal Skorokhod Embedding

The left-curtain martingale coupling in the presence of atoms

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