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Related papers: Local Volatility Calibration by Optimal Transport

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This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm \cite{Leland}. We prove several limit…

Mathematical Finance · Quantitative Finance 2015-07-10 Thai Huu Nguyen , Serguei Pergamenshchikov

This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…

Mathematical Finance · Quantitative Finance 2016-10-06 Christopher W. Miller

We prove the Duality Theorems for the stochastic optimal transportation problems with a convex cost function without a regularity assumption that is often supposed in the proof of the lower semicontinuity of an action integral. In our new…

Probability · Mathematics 2021-01-18 Toshio Mikami

Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…

Numerical Analysis · Mathematics 2025-08-19 Alexandre Caboussat , Anna Peruso

Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…

Numerical Analysis · Mathematics 2017-03-08 Jun Kitagawa , Quentin Mérigot , Boris Thibert

This paper is concerned with the existence of globally smooth solutions for the second boundary value problem for Monge-Ampere equations and the application to regularity of potentials in optimal transportation. The cost functions satisfy a…

Analysis of PDEs · Mathematics 2007-06-13 Neil S Trudinger , Xu-jia Wang

In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…

Numerical Analysis · Mathematics 2020-09-29 Enrico Facca , Michele Benzi

We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…

Pricing of Securities · Quantitative Finance 2020-07-29 Marc Lagunas-Merino , Salvador Ortiz-Latorre

We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two…

Optimization and Control · Mathematics 2024-04-01 Joshua Zoen-Git Hiew , Luca Nenna , Brendan Pass

We present an adaptation of the MA-LBR scheme to the Monge-Amp{\`e}re equation with second boundary value condition, provided the target is a convex set. This yields a fast adaptive method to numerically solve the Optimal Transport problem…

Numerical Analysis · Mathematics 2018-07-19 Jean-David Benamou , Vincent Duval

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward…

Probability · Mathematics 2008-12-10 Friedrich Hubalek , Jan Kallsen , Leszek Krawczyk

In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…

Optimization and Control · Mathematics 2026-05-22 Bahar Taskesen

Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…

Optimization and Control · Mathematics 2025-02-13 Tianhao Wu , Qihao Cheng , Zihao Wang , Chaorui Zhang , Bo Bai , Zhongyi Huang , Hao Wu

Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…

Numerical Analysis · Mathematics 2022-06-28 Said Kerrache , Yasushi Nakauchi

We solve the martingale optimal transport problem for cost functionals represented by optimal stopping problems. The measure-valued martingale approach developed in ArXiv: 1507.02651 allows us to obtain an equivalent infinite-dimensional…

Probability · Mathematics 2017-11-27 Erhan Bayraktar , Alexander Cox , Yavor Stoev

In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to…

Statistics Theory · Mathematics 2022-03-18 Adrien Vacher , François-Xavier Vialard

In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…

Statistics Theory · Mathematics 2025-03-05 XinWei Feng , Yu Jiang , Zhi Liu , Zhe Meng

We study the most common image and informal description of the optimal transport problem for quadratic cost, also known as the second boundary value problem for the Monge--Amp\`{e}re equation -- What is the most efficient way to fill a hole…

Analysis of PDEs · Mathematics 2022-07-12 Yash Jhaveri , Ovidiu Savin

We consider a spatially distributed demand for electrical vehicle recharging, that must be covered by a fixed set of charging stations. Arriving EVs receive feedback on transport times to each station, and waiting times at congested ones,…

Optimization and Control · Mathematics 2024-04-02 Fernando Paganini , Andres Ferragut

We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear…

Mathematical Finance · Quantitative Finance 2025-11-19 Andrei Cozma , Matthieu Mariapragassam , Christoph Reisinger