We derive optimality conditions and calculate approximate solutions to the problem of determining the optimal speed of mean reversion to be applied to a Gaussian state variable. The optimality criterion is the minimization of the variance of the Radon-Nikodym derivative of the measure ”with mean-reversion ” with respect to the measure ”without mean-reversion ”under constraints. Our results have two main applications. First, we show that we can increase the speed of performing resimulation and sensitivity analysis in a Monte Carlo simulation. Second, we show that there is some phase delay between the optimal speed of mean-reversion and volatility. Incorporating this effect into preference modelling could contribute to solve the equity premium puzzle in finance.