Risk analysis for a stochastic cash management model with two types of customers

A stochastic cash management system is studied in which the cash flow is modeled by the superposition of a Brownian motion with drift and a compound Poisson process with positive and negative jumps for “big” deposits and withdrawals, respectively. We derive explicit formulas for the distributions of the bankruptcy time, the time until bankruptcy or the reaching of a prespecified level, the maximum cash amount in the system, and for the expected discounted revenue generated by the system.