Optimal impulse control for cash management with quadratic holding-penalty costs (Q1862733)

The stochastic cash balance problem concerns the optimal monitoring of a cash fund which fluctuates randomly because it collects various types of income and is used as a source to make operating disbursements. The problem is to minimize the discounted expected sum of all the costs associated with this cash balance problem. Here, a general formulation of the cash balance problem is given where attention is focused on the financial management of the liquid (and essentially risk-free) assets of a firm. Optimal impulse control is studied for an infinite horizon cash management problem with the cash fund fluctuating as a Browninan motion. The main result is that there is always an optimal control for the cash management model with quadratic holding-penalty costs (there are fixed and proportional transaction costs), and that it has always the form of a control band policy.