Gaussian cubature: A practitioner's guide
Accurate modeling of management and economic processes often requires that researchers accurately approximate the expectations of functions of random variables. While commonly employed, Monte Carlo simulation techniques generally require large sample sizes to insure accuracy. For functions that are computationally burdensome, the Monte Carlo approach may be impractical. We propose a method to generate samples from multivariate distributions that contain far fewer points than reliable Monte Carlo samples, yet retain much of the original distributions' information. Our method, Gaussian cubatures generated via linear programming, is designed to be feasible for joint, but independent distributions. While heuristic for joint, dependent distributions, this method appears to be very reliable and to accurately approximate expectations of an important class of functions. (c) 2006 Elsevier Ltd. All rights reserved.
gaussian cubature monte carlo multivariate probability distributions numerical integration risk modeling