THE FUNDS MARKET BANK PROBLEM

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. T he o ptimal s trategy of the bank is explicitly found and it has the following structure: when bank reserve lower to an exogenously threshold level the bank has to purchase funds; when bank reserve tops an endogenously threshold level the bank has to sell funds.