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We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
In this article, we advocate the ensemble approach for variable selection. We point out that the stochastic mechanism used to generate the variable-selection ensemble (VSE) must be picked with care. We construct a VSE using a stochastic…
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…
Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
Credit value adjustment (CVA) is the charge applied by financial institutions to the counterparty to cover the risk of losses on a counterpart default event. In this paper we estimate such a premium under the Bates stochastic model (Bates…
Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…
We discuss the issue of estimating large-scale vector autoregressive (VAR) models with stochastic volatility in real-time situations where data are sampled at different frequencies. In the case of a large VAR with stochastic volatility, the…
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…
The aim of this paper is to describe a new an integrated methodology for project control under uncertainty. This proposal is based on Earned Value Methodology and risk analysis and presents several refinements to previous methodologies.…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
The calculation of physical quantities by lattice QCD simulations requires in some important cases the determination of the inverse of a very large matrix. In this article we describe how stochastic estimator methods can be applied to this…
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for…
In Variational Inference (VI), coordinate-ascent and gradient-based approaches are two major types of algorithms for approximating difficult-to-compute probability densities. In real-world implementations of complex models, Monte Carlo…
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…
This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Predicting future values at risk (fVaR) is an important problem in finance. They arise in the modelling of future initial margin requirements for counterparty credit risk and future market risk VaR. One is also interested in derived…