Approximation of Wiener integrals with respect to the Brownian bridge by simulation of SDEs

Numerical integration of stochastic differential equations together with the Monte Carlo technique is used to evaluate conditional Wiener integrals of exponential-type functionals. An explicit Runge-Kutta method of order four and implicit Runge-Kutta methods of order two are constructed. The corresponding convergence theorems are proved. To reduce the Monte Carlo error, a variance reduction technique is considered. Results of numerical experiments are presented