Monte carlo evaluation of functionals of solutions of stochastic differential equations. variance reduction and numerical examples

Abstract

Variance–reducing estimators are derived for functionals of the solution of the general Ito stochastic differential equation. These estimators allow to apply variance reduction techniques known from the Monte Carlo theory. In particular, variance–reducing Euler estimators are constructed as well as variance–reducing unbiased estimators. Numerical examples are given. They show that the variance reduction techniques cause an enormous gain in efficiency, reducing the statistical error up to 50 times. They also demonstrate the effect of the unbiased estimators, which allow to evaluate the functionals without reducing the time step.