Change of numeraire in the two-marginals martingale transport problem

Campi, Luciano; Laachir, Ismail; Martini, Claude

doi:10.48550/arxiv.1406.6951

Cited by 2 publications

(2 citation statements)

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“…du for all z ≥ 0; then Assumption 2.1crucial in Hobson and Klimmek's analysis-is equivalent to ∆ having a single maximiser [7,Lemma 5.1]. This assumption imposes constraints on the tail behaviour of the difference between the two laws µ and ν, and is clearly satisfied, for instance, in the Black-Scholes case.…”

Section: Primal Solution For the At-the-money Casementioning

confidence: 99%

No-arbitrage bounds for the forward smile given marginals

Badikov

Jacquier

Liu

et al. 2017

Quantitative Finance

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Abstract. We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can consider the dual problem, consisting in finding optimal martingale measures under which the upper and the lower bounds are attained. Semi-analytical solutions to this dual problem were proposed by Hobson and Klimmek [14] and by Hobson and Neuberger [15]. We recast this dual approach as a finite dimensional linear programme, and reconcile numerically, in the Black-Scholes and in the Heston model, the two approaches.

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Section: Primal Solution For the At-the-money Casementioning

confidence: 99%

No-arbitrage bounds for the forward smile given marginals

Badikov

Jacquier

Liu

et al. 2017

Quantitative Finance

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show abstract

“…The opposite direction is taken in [3], where Skorokhod embeddings are studied from an optimal transport point of view. Recently, a rich literature has emerged around the topics of model robustness and transport; see, e.g., [1,8,13,14,15,16,22,35] for models in discrete time and [6,11,18,17,20,21,24,25,32,34,36,38,40] for continuous-time models.…”

Section: Introductionmentioning

confidence: 99%

Complete duality for martingale optimal transport on the line

Beiglböck¹,

Nutz²,

Touzi³

2017

Ann. Probab.

111

171

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We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a duality gap and existence of dual optimizers. Both properties are shown to fail in the classical formulation. As a consequence of the duality result, we obtain a general principle of cyclical monotonicity describing the geometry of optimal transports.

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Change of numeraire in the two-marginals martingale transport problem

Cited by 2 publications

References 0 publications

No-arbitrage bounds for the forward smile given marginals

No-arbitrage bounds for the forward smile given marginals

Complete duality for martingale optimal transport on the line

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