arXiv research

We extend martingale transport results to weak martingale transport.

Extends optimal transport to dynamic and martingale settings.

Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $π_1, π_2, \ldots$ converges weakly to a transport plan $π$, then $π$ is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for th…

The study establishes stability in WMOT, crucial for finance with imprecise data.

Extends martingale transport for robust finance problems.

Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.

The paper introduces a new method for risk measurement using weak optimal transport.

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present…

Dynamic reinsurance aims to minimize surplus risk using martingale transport.

The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the…

Efficiently computes robust option prices using multi-marginal martingale transport.

Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Sev…

Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be approximated using linear programming (LP) problems which result from a discretisa…

Existence proved for $q$-Bass martingales with specific marginals.

New approach shows continuity and compactness of martingale measures.

Study bounds financial path expectations using martingale distributions.

Study on convergence rates for optimal transport with regularization.

This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network wi…

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…

In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative adversarial networks. As some additional applications, we consider anomaly detection and …

Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.

Gradient flow method solves for optimal transport starting distributions.

We determine the optimal structure of couplings for the \emph{Martingale transport problem} between radially symmetric initial and terminal laws $μ, ν$ on $\R^d$ and show the uniqueness of optimizer. Here optimality means that such solutions will minimize the functional $\E |X-Y|^p$ where $0<p \leq 1$, and the dimensio…

The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints…

Unified RMOT framework for non-modelable risk factors reduces audit bounds.

We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption, which restricts the variability of the forward-looking transitions of the martingal…

New method finds closest martingale to Brownian motion.

Paper develops MMOT framework for financial applications with neural acceleration.

Study uses weak transport for non-convex costs in fixed-income markets.

Study optimal transport on globally hyperbolic spacetimes, focusing on weak Kantorovich potentials' regularity.

We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod e…

Consider a multiperiod optimal transport problem where distributions $μ_{0},\dots,μ_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\simμ_{t}$. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property…

New deep learning architecture learns martingales efficiently.

Deep learning for financial derivatives pricing and hedging.

Paper reduces dimensionality for robust option pricing in 2-asset markets.

In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan constructed in \cite{HobsonKlimmek2013} as well as the one introduced in \cite{BeiglJuil} and further studi…

The study examines how including additional call option prices affects model-independent price bounds for exotic derivatives.

NOT learns optimal transport plans, kernel costs improve performance.

A new method for averaging probability distributions based on optimal weak mass transport.

In classical optimal transport, the contributions of Benamou-Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas. We suggest a Benamou-Brenier type formulation of the martingale transport proble…

We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $γ$ is optimal if and only if there is a maximal monotone set $G$ that supports the $x$-marginal of $γ$ and such tha…

A new relaxed framework for pricing illiquid derivatives using bid-ask spreads.

In credit risk literature, the existence of an equivalent martingale measure is stipulated as one of the main assumptions in the hazard process model. Here we show by construction the existence of a measure that turns the discounted stock and defaultable bond prices into martingales by identifying a no-arbitrage condit…

Unique solutions found for diffusive martingale problems.

Study dynamic trading in options to improve price bounds for exotic derivatives.

Enhances MOT with causality constraints for better option pricing.