Operational Risk Management: Optimal Inspection Policy

Major banks around the world lost nearly $210 billion during the period of 2011-2016 due to operational risk events. To mitigate the severe consequences that can arise from such events, the Basel Regulatory Committee has mandated that financial institutions worldwide conduct inspections on operational risk. In light of the importance of operational risk and its current regulation in the industry, this paper proposes a continuous-time principal -agent model that explores the optimal inspection policy of a financial firm (principal) and the effort of its employees (agent) to reduce the occurrence of risk events. First, we characterize the optimal inspection strategy under two commonly used policies in practice, namely random and periodic policies. This characterization reveals the conditions for two different modes of inspection (effort inducement and error correction), as well as the nuanced interactions among the inspection frequency, the penalty charged for errors, and the wage paid to employees. Next, by comparing random and periodic policies, we find that the random policy outperforms the periodic policy if and only if the inspection cost is high. Furthermore, we propose a hybrid policy that strictly dominates the random policy and weakly dominates the periodic policy, suggesting that a proper reduction of the random element in the inspection policy, in the manner of our proposed hybrid policy, can always improve its performance. Finally, we examine the complete information benchmark (without moral hazard), supplemental mitigation strategies, and numerical studies to provide further insights and show the robustness of our main findings.