Related papers: Approximation of martingale couplings on the line …
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…
We study the martingale optimal transport problem with state-dependent trading frictions and develop a geometric and duality framework extending from the one time-step to the multi-marginal setting. Building on the left-monotone structure…
Martingale Optimal Transport (MOT) provides a framework for robust pricing and hedging of illiquid derivatives. Classical MOT enforces exact calibration of model marginals to the mid-prices of vanilla options. Motivated by the industry…
Strassen's theorem asserts that for given marginal probabilities $\mu,\nu$ there exists a martingale starting in $\mu$ and terminating in $\nu$ if and only if $\mu,\nu$ are in convex order. From a financial perspective, it guarantees the…
We study Sinkhorn's algorithm for solving the entropically regularized optimal transport problem. Its iterate $\pi_{t}$ is shown to satisfy $H(\pi_{t}|\pi_{*})+H(\pi_{*}|\pi_{t})=O(t^{-1})$ where $H$ denotes relative entropy and $\pi_{*}$…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
It was shown by the authors that two one-dimensional probability measures in the convex order admit a martingale coupling with respect to which the integral of $\vert x-y\vert$ is smaller than twice their $\mathcal W_1$-distance…
We present a machine learning approach for finding minimal equivalent martingale measures for markets simulators of tradable instruments, e.g. for a spot price and options written on the same underlying. We extend our results to markets…
The (left-)curtain coupling, introduced by Beiglb\"ock and the author is an extreme element of the set of "martingale" couplings between two real probability measures in convex order. It enjoys remarkable properties with respect to order…
We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plugin estimator based on empirical measures and show it is consistent but lacks suitable…
We consider the problem of finding consistent upper price bounds and super replication strategies for exotic options, given the observation of call prices in the market. This field of research is called model-independent finance and has…
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…
It is well known that martingale transport plans between marginals $\mu\neq\nu$ are never given by Monge maps -- with the understanding that the map is over the first marginal $\mu$, or forward in time. Here, we change the perspective, with…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
We introduce a constrained optimal transport problem where origins $x$ can only be transported to destinations $y\geq x$. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect $Y-X$ given…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…
This note contains a short discussion on the sufficiency of finite optimality in martingale transport. It is shown that finitely minimal martingale measures are solutions of the martingale transport problem when the cost function is upper…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
We establish novel quantitative stability results for optimal transport problems with respect to perturbations in the target measure. We provide explicit bounds on the stability of optimal transport potentials and maps, which are relevant…