Optimal Changes of Gaussian Measures, with Application to Finance

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.