Liquidity management of foreign exchange reserves in continuous time

In order to cope with daily foreign currency exchange payments or trades and avoid liquidity crisis, central banks need to maintain the liquidity of foreign exchange reserves. In this paper, we develop a Foreign Exchange Reserves Liquidity Management (FERLM) model based on stochastic process by introducing a foreign exchange factor. We also generate a feasible target proportion of the liquidity reserve to total foreign exchange reserves, by seeking the balance between capital gains of holding foreign exchange reserves and losses of liquidity insufficiency.