Change of numeraire in the two-marginals martingale transport problem

DOI10.1007/s00780-016-0322-2zbMath1369.91174arXiv1406.6951OpenAlexW1537865873WikidataQ59603443 ScholiaQ59603443MaRDI QIDQ522059

Ismail Laachir, Claude Martini, Luciano Campi

Publication date: 13 April 2017

Published in: Finance and Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.6951

zbMATH Keywords

change of numerairerobust hedgingmodel uncertaintyoptimal transportmodel-independent pricingforward start straddle

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Martingales with continuous parameter (60G44) Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items (23)

Canonical supermartingale couplings ⋮ Geometry of distribution-constrained optimal stopping problems ⋮ No-arbitrage bounds for the forward smile given marginals ⋮ Monotone martingale transport plans and Skorokhod embedding ⋮ The geometry of multi-marginal Skorokhod embedding ⋮ Weak transport for non‐convex costs and model‐independence in a fixed‐income market ⋮ Dual attainment for the martingale transport problem ⋮ Supermartingale Brenier's theorem with full-marginals constraint ⋮ Quantization and martingale couplings ⋮ Supermartingale shadow couplings: the decreasing case ⋮ A potential-based construction of the increasing supermartingale coupling ⋮ All adapted topologies are equal ⋮ Martingale Benamou-Brenier: a probabilistic perspective ⋮ ROBUST BOUNDS FOR DERIVATIVE PRICES IN MARKOVIAN MODELS ⋮ Monotonicity preserving transformations of MOT and SEP ⋮ An explicit martingale version of the one-dimensional Brenier's theorem with full marginals constraint ⋮ Tightening robust price bounds for exotic derivatives ⋮ Compactness criterion for semimartingale laws and semimartingale optimal transport ⋮ Shadow couplings ⋮ Adapted Wasserstein distances and stability in mathematical finance ⋮ Convex order, quantization and monotone approximations of ARCH models ⋮ A construction of the left-curtain coupling ⋮ Stability of martingale optimal transport and weak optimal transport

Cites Work

• On a problem of optimal transport under marginal martingale constraints
• An explicit martingale version of the one-dimensional Brenier theorem
• Model-independent bounds for option prices -- a mass transport approach
• Martingale optimal transport and robust hedging in continuous time
• Robust price bounds for the forward starting straddle
• Martingale optimal transport in the Skorokhod space
• Mathematical methods for financial markets.
• Robust hedging of the lookback option
• Complete duality for martingale optimal transport on the line
• The Skorokhod Embedding Problem and Model-Independent Bounds for Option Prices
• Changes of numéraire, changes of probability measure and option pricing
• Asymptotics of Forward Implied Volatility
• The Existence of Probability Measures with Given Marginals

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