This paper considers the problem faced by a bank which trades in the funds
market so as to maintain the reserve requirements and minimize the costs of
doing that. We work in a stochastic paradigm and the reserve requirements are
determined by the demand deposit process, modelled as a geometric Brownian
motion. The discount rates for the cumulative funds purchased and the
cumulative funds sold are assumed to be different. The optimal strategy of the
bank is explicitly found and it has the following structure: when bank reserves
lower to an exogenously threshold level the bank has to purchase funds; when
bank reserves tops an endogenously threshold level the bank has to sell funds