Monte Carlo Methods

Abstract

The term ‘Monte Carlo methods’ is used to refer to two different, though closely related, techniques. The first meaning, currently the less common one among economists, is the evaluation of definite integrals by use of random variables. The idea is to evaluate ${\int}_a^bF(x)\mathrm{d}x$ (where x may be a vector) by estimating ${\int}_a^b\left[F(x)p(x)\right]p(x)\mathrm{d}x$^. Here p(x) is the density function of a random variable defined over [a, b]. The original problem has been converted into one of estimating the mean of F(x)/p(x). It can be solved by using a random sample drawn from p(x) and calculating the average value of F(x)/p(x).