Martingale optimal transport duality

Cheridito, Patrick; Kiiski, Matti; Prömel, David J.; Soner, H. Meté

doi:10.1007/s00208-019-01952-y

Cited by 33 publications

(24 citation statements)

References 61 publications

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“…Hence the result is not only of interest for a "small" prediction set, but also for "large" ones, e.g., the set Ξ of all paths which possess a quadratic variation and are Hölder continuous. During the reviewing process of this work, a similar duality theorem in the context of martingale optimal transport on the space of càdlàg paths has been obtained in [7]. Under a suitable constructed topology on the space of càdlàg paths, the duality result in [7] has also been established by enlarging the set of admissible strategies using the lim inf-closure in the spirit of [34] and then extending the duality result from semicontinuous claims to Borel measurable ones following the approach in [17] to apply Choquet's capacitability theorem.…”

Section: Superhedging Duality For Prediction Sets Closed Under Stoppingmentioning

confidence: 89%

Pathwise superhedging on prediction sets

Bartl

Kupper

Neufeld³

2019

Finance Stoch

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In this paper we provide a pricing-hedging duality for the model-independent superhedging price with respect to a prediction set Ξ ⊆ C[0, T ], where the superhedging property needs to hold pathwise, but only for paths lying in Ξ. For any Borel measurable claim ξ which is bounded from below, the superhedging price coincides with the supremum over all pricing functionals E Q [ξ] with respect to martingale measures Q concentrated on the prediction set Ξ. This allows to include beliefs in future paths of the price process expressed by the set Ξ, while eliminating all those which are seen as impossible. Moreover, we provide several examples to justify our setup. .sg. setting, superhedging is required to hold true for every possible future path in C[0, T ] of the price process. Such an approach has started with the seminal work [14] and has been recently lead to attention in various other works; we refer to [1,3,6,10], to name but a few.However, it turns out that the concept of superhedging is too robust leading to too high prices. In fact, for stochastic volatility or rough volatility models, it turns out that the classical superhedging price coincides with the model-independent one and is so high that for Markovian payoffs of the form Γ(S T ), like e.g. the European Call and Put option, the optimal superhedging strategy can be chosen to be of buy-and-hold type, see [9,23]. To reduce the model-independent superhedging price, inspired by the work of [22], [15] introduced the concept of prediction sets, where agents may allow to exclude paths which they consider to be impossible to model future price paths. Hence they require the superhedging property only to hold true on every path in Ξ ⊆ C[0, T ] of their prediction set.Whereas the pricing-hedging duality is well-understood for the pathwise superhedging with respect to all paths in C[0, T ], it turns out that the problem becomes considerably more difficult when requiring the superhedging property only to hold true on the prediction set Ξ ⊆ C[0, T ]. To illustrate the difficulty, consider the examples where the agent may believe in the Black-Scholes model, or is uncertain about the volatility like in the G-expectation (see [28]) and hence models his/her beliefs by requiring

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Section: Superhedging Duality For Prediction Sets Closed Under Stoppingmentioning

confidence: 89%

Pathwise superhedging on prediction sets

Bartl

Kupper

Neufeld³

2019

Finance Stoch

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“…Motivated by the robust model-independent pricing problem, the martingale optimal transport (MOT) has received considerable attention, see [29,21,9,19,17]. We also refer to [31,18,22] for the multidimensional case and to [8,13] for connections to Skorokhod problem.…”

Section: Wmot-framework and Main Resultsmentioning

confidence: 99%

Stability of the Weak Martingale Optimal Transport Problem

Beiglböck¹,

Jourdain²,

Margheriti³

et al. 2021

Preprint

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While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali [25] this corresponds to weak martingale optimal transport (WMOT).In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the underlying marginals. As application, we deduce the stability of the superreplication bound for VIX futures as well as the stability of stretched Brownian motion and we derive a monotonicity principle for WMOT.

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“…This work was initiated by investigations in robust pricing of derivative contracts by Guo et al [24,Lemma 3.7] and the current author together with Cheridito et al [12,Corollary 6.7]. In parallel work [12], we describe a general superhedging/ sublinear-pricing paradigm and its relation to the compactness studied in the present work.…”

Section: Motivation By the Analysis Of A Problem In Financementioning

confidence: 91%

“…This is the so-called martingale optimal transport problem studied e.g. in the aforementioned works of [3,15,24,12].…”

Section: Motivation By the Analysis Of A Problem In Financementioning

confidence: 99%

The Riesz representation theorem and weak∗ compactness of semimartingales

Kiiski

2020

Finance Stoch

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We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform tightness condition is a weak∗ compact set of semimartingale measures in the dual pairing of bounded continuous functions and Radon measures, that is, the dual pairing from the Riesz representation theorem under topological assumptions on the path space. Similar results are obtained for quasi- and supermartingales under analogous conditions. In particular, we give a full characterisation of the strongest topology on the Skorokhod space for which these results are true.

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Martingale optimal transport duality

Cited by 33 publications

References 61 publications

Pathwise superhedging on prediction sets

Pathwise superhedging on prediction sets

Stability of the Weak Martingale Optimal Transport Problem

The Riesz representation theorem and weak∗ compactness of semimartingales

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