Optimal management of international reserves

Abstract

This article develops a continuous time stochastic model for determining the optimal international reserves management policy when the data generating process of international reserves is a geometric Brownian motion. The policy is a two-parameter control-limit that consists of an appropriate and a ceiling level on reserves holdings, given an exogenous floor on international reserves. The optimal solution is determined so as to minimize the total costs of international reserves holdings. It is proved that our results extend the framework of Frenkel and Jovanovic when the logarithm of international reserves is an arithmetic Brownian motion. We also explain that Jung paper does not extend Frenkel and Jovanovic model as claimed by the former. The model is calibrated to derive the optimal level and liquidity tranche size upper bound of international reserves of the CEMAC monetary union.