Related papers: Path Dependent Optimal Transport and Model Calibra…
We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et…
We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension…
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…
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…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results…
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
In this article, we present a general methodology for control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main result of this…
Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) that arise in pricing…
We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…
The diffusive transport distance, a novel pseudo-metric between probability measures on the real line, is introduced. It generalizes Martingale optimal transport, and forms a hierarchy with the Hellinger and the Wasserstein metrics. We…
We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under…
Motivated by recent developments in the calibration of stochastic volatility models (SVMs for short), we study continuous-time formulations of martingale optimal transport and martingale Schr\"odinger bridge problems. We establish duality…
The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…
In the current book I suggest an off-road path to the subject of optimal transport. I tried to avoid prior knowledge of analysis, PDE theory and functional analysis, as much as possible. Thus I concentrate on discrete and semi-discrete…
Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are…