Related papers: Efficient Least Squares Monte-Carlo Technique for …
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…
In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
We introduce a new method to calculate the credit exposure of European and path-dependent options. The proposed method is able to calculate accurate expected exposure and potential future exposure profiles under the risk-neutral and the…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…
Monte Carlo methods, such as Markov chain Monte Carlo (MCMC), remain the most regularly-used approach for implementing Bayesian inference. However, the computational cost of these approaches usually scales worse than linearly with the…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
Since its formulation in the late 1940s, the Feynman-Kac formula has proven to be an effective tool for both theoretical reformulations and practical simulations of differential equations. The link it establishes between such equations and…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We leverage multilevel Monte Carlo (MLMC) to improve the performance of multi-step look-ahead Bayesian optimization (BO) methods that involve nested expectations and maximizations. Often these expectations must be computed by Monte Carlo…
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…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume…
A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the…