Geometric Mean Reversion : Formulas for the Equilibrium Density and Analytic Moment Matching

We study the classical geometric mean reversion process which has been used to model commodity prices by various authors in Economics and Finance. We obtain certain regularity results which guarantee positivity and the existence of a stationary distribution. More important we derive an analytical formula for the stationary distribution and all of its higher moments. Furthermore we derive a computationally simple but efficient recursive formula for the higher moments which we apply to moment matching