Related papers: Convexity adjustments \`a la Malliavin
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…
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…
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,…
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…
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…
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…
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…
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,…
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…
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…
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…
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.
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…
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…
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…
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…
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…
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…
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…
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…