Operational Risk Management: A Stochastic Control Framework with Preventive and Corrective Controls

In this paper, we propose a general modeling framework for operational risk management of financial firms. We consider operational risk events as shocks to a financial firm’s value process and then study capital investments under preventive and corrective controls to mitigate risk losses. The optimal decisions are made in three scenarios: (i) preventive control only, (ii) corrective control only, and (iii) joint controls. We characterize the optimal control policies within a general modeling framework that comprises these three scenarios and then discuss an exponential risk reduction function. We conclude our work with an application of our model to a data set from a commercial bank. We find that, through a proper investment strategy, we can achieve a significant performance improvement, especially when the risk severity level is high. Moreover, with controls, the value of the firm tends to increase relative to the value of the firm without controls. Hence, the controls are essentially smoothing out the jump losses and increasing the value of the firm. At the bank we analyze we find that with a joint control strategy the bank can achieve profit increases from 7.45% to 11.62% when the risk reduction efficiencies of the two controls are high. In general, our modeling framework, which combines a typical operational risk process with stochastic control, may suggest a new research direction in operations management and operational risk management.