Related papers: Control variate selection for Monte Carlo integrat…
Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To…
We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration. So far, the core challenge of applying the method of control variates has been finding a good approximation of the integrand…
Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
This paper presents a method to leverage arbitrary neural network architecture for control variates. Control variates are crucial in reducing the variance of Monte Carlo integration, but they hinge on finding a function that both correlates…
Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but…
The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable to…
There are no known exact formulas for the valuation of a number of exotic options, and this is particularly true for options under discrete monitoring and for American style options. Therefore, one usually recourses to a Monte Carlo…
A general methodology is presented for the construction and effective use of control variates for reversible MCMC samplers. The values of the coefficients of the optimal linear combination of the control variates are computed, and adaptive,…
A novel linear integration rule called $\textit{control neighbors}$ is proposed in which nearest neighbor estimates act as control variates to speed up the convergence rate of the Monte Carlo procedure on metric spaces. The main result is…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency…
Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand,…
Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution.…
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level…
We investigate the use of Antithetic Variables, Control Variates and Importance Sampling to reduce the statistical errors of option sensitivities calculated with the Likelihood Ratio Method in Monte Carlo. We show how Antithetic Variables…
Bayesian model comparison relies upon the model evidence, yet for many models of interest the model evidence is unavailable in closed form and must be approximated. Many of the estimators for evidence that have been proposed in the Monte…
Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating a…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…