Martingale optimal transport and robust hedging in continuous time

By Yan Dolinsky, H. M. Soner. Probability theory and related fields, 2012

243 citations recorded by the source corpus.

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge–Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

Subfields: Finance, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d28b22db6f6bfe19a20037a3113ba4e7c315cf93

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Geometry and Topology

Citations in the corpus

Stochastic control for a class of nonlinear kernels and applications (2015, background): “2) with r = 0, and where the set of measures considered satisfy the predictable martingale representation property (that is the financial market is complete under any of the measures considered) this superhedging price has been thoroughly studied in the recent literature, see among others [2, 6, 25,”
ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES (2014, background): “A related setting is considered in Dolinsky and Soner (2014a) where S is the canonical process in the space of continuous paths.”
All adapted topologies are equal (2019, unknown): “[34, 13, 27, 23, 17, 33, 18, 12, 14] among many others).”
Optimal transport and Skorokhod embedding (2013, background): “The first papers to study such problems include [7,19,23,32], and this field is commonly referred to as martingale optimal transport.”
Stability of martingale optimal transport and weak optimal transport (2019, unknown): “tter class of problems from this viewpoint. 1.1. Stability of martingale optimal transport. The martingale optimal transport problem is a variant of (OT) stemming from robust mathematical ﬁnance (cf. [29, 14, 38, 21, 20, 17, 12, 8, 31, 32, 35, 19, 30, 22, 27] among many others). In order to deﬁne th”
Model-free superhedging duality (2015, unknown): “The reformulation of the superhedging duality in the framework of optimal mass transport led to important results both in discrete and continuous time as in [3, 11, 12, 14, 15, 20, 23].”
Arbitrage and duality in nondominated discrete-time models (2013, background): “The authors thank Mathias Beiglböck and Jan Obłój for their constructive comments.”
UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY IN DISCRETE TIME (2013, background): “The robust superhedging problem has been studied in several settings; see [1, 4, 6, 11, 13, 17, 23, 26, 32, 33], among others.”
The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, background): “A proof of one technical lemma is relegated to the Appendix.”
Complete Duality for Martingale Optimal Transport on the Line (2015, background): “, [1, 8, 12, 13, 14, 19, 33] for models in discrete time and [6, 10, 15, 17, 18, 21, 22, 29, 31, 32, 35, 37] for continuous-time models.”
On a problem of optimal transport under marginal martingale constraints (2012, methodology): “Duality results for a continuous time martingale transport problem are obtained by Galichon, Henry-Labordere, Touzi [10] and Dolinsky and Soner [7].”
Causal transport plans and their Monge–Kantorovich problems (2013, background): “Over the last decade, connections between optimal transport and stochastic calculus have received contributions of several origins (among many, see [7, 21, 24, 34]) in continuation of a long history (for instance, see [28–30] and the references therein), with applications to fields such as financial”
Pathwise stochastic integrals for model free finance (2013, methodology): “One was proposed by [15], who simply restrict themselves to trading strategies (integrands) of bounded variation.”
Structure of optimal martingale transport plans in general dimensions (2015, unknown): “The dynamic case have been also studied by Galichon-Henri-Labordere-Touzi [14] and Dolinsky–Soner [10, 11].”