Monte Carlo Simulation and Improvement of Variance Reduction Techniques

Variance reduction technique is an important method to improve the efficiency of Monte Carlo simulation. In order to research the principle of reducing variance, we introduce Monte Carlo simulation firstly; then enumerate several commonly used methods of variance reduction and furtherly combine them to study whether it improves the simulation performance; lastly, we write programs to compare the reduction rates of different methods on the same problem. It turns out that variance reduction techniques have remarkable effect on increasing the calculation accuracy and reducing the calculation time of Monte Carlo simulation. And the combination of multiple variance reduction techniques is more effective in practical application.