Variance Reduction Method

Variance reduction techniques aim to decrease the mean-square error of a Monte Carlo estimate without necessarily increasing the number of samples. For an estimate of the mean value, the error is given by:

$$\mathbb{E}\left[{\left|\mu -{\hat{\mu }}_K\right|}^2\right]=\mathbb{V}\left[{\hat{\mu }}_K\right]=\frac{\mathbb{V}[Y]}{K}.$$

Reducing the variance $\mathbb{V}[Y]$ directly improves the accuracy of the simulation.

Examples of variance reduction methods

• Control Variate Method
• Multilevel Monte Carlo (MLMC)