We consider two Gaussian measures. In the “initial”measure the state variable is Gaussian, with zero drift andtime-varying volatility. In the “target measure” the statevariable follows an Ornstein-Uhlenbeck process, with a free set ofparameters, namely, the time-varying speed of mean reversion. Welook for the speed of mean reversion that minimizes the varianceof the Radon-Nikodym derivative of the target measure with respectto the initial measure under a constraint on the time integral ofthe variance of the state variable in the target measure. We showthat the optimal speed of mean reversion follows a Riccatiequation. This equation can be solved analytically when thevolatility curve takes specific shapes. We discuss an applicationof this result to simulation, which we presented in an earlierarticle.
展开▼
