Some Results on Skorokhod Embedding and Robust Hedging with Local Time

Claisse, Julien; Guo, Gaoyue; Henry-Labordère, Pierre

doi:10.1007/s10957-017-1201-5

Cited by 8 publications

(4 citation statements)

References 25 publications

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“…) using the same arguments for B m , and obtain thus (14). Alternatively, assume that the third condition holds.…”

Section: Deterministic Discretizationmentioning

confidence: 85%

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Computational methods for martingale optimal transport problems

Guo¹,

Obłój²

2019

Ann. Appl. Probab.

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We develop computational methods for solving the martingale optimal transport (MOT) problem -a version of the classical optimal transport with an additional martingale constraint on the transport's dynamics. We prove that a general, multi-step multi-dimensional, MOT problem can be approximated through a sequence of linear programming (LP) problems which result from a discretization of the marginal distributions combined with an appropriate relaxation of the martingale condition. We further furnish two generic approaches for discretizing probability distributions, suitable respectively for the cases when we can compute integrals against these distributions or when we can sample from them. These render our main result applicable and lead to an implementable numerical scheme for solving MOT problems. Finally, specializing to the one-step model on real line, we provide an estimate of the convergence rate which, to the best of our knowledge, is the first of its kind in the literature. for insightful discussions and comments. † The second author also gratefully acknowledges support from St John's College, Oxford. MSC 2010 subject classifications: Primary 49M25, 60H99; secondary 90C08. 1 imsart-aap ver.

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“…) using the same arguments for B m , and obtain thus (14). Alternatively, assume that the third condition holds.…”

Section: Deterministic Discretizationmentioning

confidence: 85%

“…It is also worth mentioning that some concrete MOT problems for particular payoffs have been investigated, by means of stochastic control or Skorokhod embedding techniques, in a stream of papers going back to Hobson [29], see e.g. [9,14,23,12,15,16,30,31,27].…”

Section: Introductionmentioning

confidence: 99%

Computational methods for martingale optimal transport problems

Guo¹,

Obłój²

2019

Ann. Appl. Probab.

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“…Applying the method of pathwise inequalities established in [8] and [9], we verify the optimality of τ by constructing the dual optimizer (G, M ). We define…”

Section: And Alsomentioning

confidence: 99%

Embedding of Walsh Brownian Motion

Bayraktar

Zhang

2019

Preprint

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Let (Z, κ) be a Walsh Brownian motion with spinning measure κ. Suppose µ is a probability measure on R n . We characterize all the κ such that µ is a stopping distribution of (Z, κ). If we further restrict the solution to be integrable, we show that there would be only one choice of κ. We also generalize Vallois' embedding, and prove that it minimizes the expectation E[Ψ(L Z τ )] among all the admissible solutions τ , where Ψ is a strictly convex function and (L Z t ) t≥0 is the local time of the Walsh Brownian motion at the origin.

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“…Moreover, the corresponding embeddings enjoys the similar optimality property as in the one-marginal case. In Claisse, Guo and Henry-Labordère [7], an extension of the Vallois solution to the two-marginals case is obtained for a specific class of marginals. We also refer to Beiglböck, Cox and Huesmann [5] for a geometric representation of the optimal Skorokhod embedding solutions given multiple marginals.…”

Section: Introductionmentioning

confidence: 99%