Related papers: Estimating option prices using multilevel particle…

We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a…

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies.…

The multilevel Monte Carlo (MLMC) method is highly efficient for estimating expectations of a functional of a solution to a stochastic differential equation (SDE). However, MLMC estimators may be unstable and have a poor (noncanonical)…

In this paper we present two parallel Monte Carlo based algorithms for pricing multi--dimensional Bermudan/American options. First approach relies on computation of the optimal exercise boundary while the second relies on classification of…

This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…

In general, the pricing of variable annuities with guarantees can be done by solving the corresponding optimal stochastic control problem if the contract withdrawal strategy is assumed to be optimal. This is typically solved as a dynamic…

Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually,…

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…

This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…

In a context of illiquidity, the reservation price is a well-accepted alternative to the usual martingale approach which does not apply. However, this price is not available in closed form and requires numerical methods such as Monte Carlo…

The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing,…

We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional…

This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is…

Particle Markov chain Monte Carlo (pMCMC) is now a popular method for performing Bayesian statistical inference on challenging state space models (SSMs) with unknown static parameters. It uses a particle filter (PF) at each iteration of an…

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity,…

Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…