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Related papers: Convexity adjustments \`a la Malliavin

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Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…

Computation · Statistics 2016-12-23 Alain Durmus , Eric Moulines , Marcelo Pereyra

An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…

Optimization and Control · Mathematics 2021-11-30 N. I. M. Gould , Ph. L. Toint

Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations combines Stein's method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. In the last decade,…

Probability · Mathematics 2021-02-16 Ehsan Azmoodeh , Giovanni Peccati , Xiaochuan Yang

In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black \& Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching…

Computational Finance · Quantitative Finance 2020-05-29 Fabio Antonelli , Alessandro Ramponi , Sergio Scarlatti

We introduce a new numerical approximation method for functionals of factor credit portfolio models based on the theory of mod-$\phi$ convergence and mod-$\phi$ approximation schemes. The method can be understood as providing correction…

Computational Finance · Quantitative Finance 2022-11-09 Pierre-Loïc Méliot , Ashkan Nikeghbali , Gabriele Visentin

In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…

Computer Science and Game Theory · Computer Science 2023-01-18 Volkan Cevher , Georgios Piliouras , Ryann Sim , Stratis Skoulakis

On August 20, 2025, GPT-5 was reported to have solved an open problem in convex optimization. Motivated by this episode, we conducted a controlled experiment in the Malliavin--Stein framework for central limit theorems. Our objective was to…

Probability · Mathematics 2025-09-04 Charles-Philippe Diez , Luis da Maia , Ivan Nourdin

Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives,…

Mathematical Finance · Quantitative Finance 2019-05-07 Anastasia Borovykh , Andrea Pascucci , Cornelis W. Oosterlee

In this paper, we describe an explicit extension formula in sensitivity analysis regarding the Malliavin weight for jump-diffusion mean-field stochastic differential equations whose local Lipschitz drift coefficients are influenced by the…

Probability · Mathematics 2025-02-04 Samaneh Sojudi , Mahdieh Tahmasebi

We introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping…

Pricing of Securities · Quantitative Finance 2015-02-23 Lorenz Schneider , Bertrand Tavin

We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…

Probability · Mathematics 2009-09-17 Ivan Nourdin , Giovanni Peccati

These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.

Probability · Mathematics 2025-02-13 Luciano Tubaro , Margherita Zanella

This paper studies function approximation for finite horizon discrete time Markov decision processes under certain convexity assumptions. Uniform convergence of these approximations on compact sets is proved under several sampling schemes…

Optimization and Control · Mathematics 2018-02-21 Jeremy Yee

We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our results generalize and refine the main…

Probability · Mathematics 2008-11-19 Ivan Nourdin , Giovanni Peccati , Anthony Réveillac

We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced…

Computation · Statistics 2024-06-24 Vishwak Srinivasan , Andre Wibisono , Ashia Wilson

An efficient discrete time and space Markov chain approximation employing a Brownian bridge correction for computing curvilinear boundary crossing probabilities for general diffusion processes was recently proposed in Liang and Borovkov…

Probability · Mathematics 2023-02-24 Vincent Liang , Konstantin Borovkov

We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…

Pricing of Securities · Quantitative Finance 2012-05-15 Jean-Pierre Fouque , Matthew Lorig

Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…

Methodology · Statistics 2026-05-11 Daniel Andrew Coulson , David S. Matteson , Martin T. Wells

Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around $\mathbb{R}\subset \mathbb{C}$. The Fourier transform techniques reduces calculation…

Computational Finance · Quantitative Finance 2018-08-17 Svetlana Boyarchenko , Sergei Levendorskiĭ

We establish a rigorous connection between pathwise (reparameterization) and score-function (Malliavin) gradient estimators by showing that both arise from the Malliavin integration-by-parts identity. Building on this equivalence, we…

Machine Learning · Computer Science 2026-02-20 Kevin D. Oden