Risk-sensitive control of cash management systems

Firms manage cash for operational, precautionary and speculative purposes. Stat-of-the-art cash management models usually focus on cost minimization by means of a set of controlling bounds. In this paper, we propose a multiobjective model to control cash management systems with multiple accounts characterized by generalized cash flow processes. In addition, we replace the customary use of bounds with cash balance reference trajectories. The model considers two objectives such as cost minimization, measured by the sum of transaction and holding costs, and risk control, measured by the sum of deviations from a given cash balance reference. We also present theoretical results on the stability of the model for deterministic, predictable and purely random cash flow processes. By means of numerical examples, we analyze the robustness of different risk-sensitive models to mean-variance misspecifications. The results show that tuning a parameter of our model can be of help to find more robust cash management policies. Finally, we present a case study showing how our risk-sensitive model can be used to adjust policies according to risk preferences.