Optimal provisioning for bank loan losses in a robust control framework

The concept of robustness started emerging in financial and economics literature in the late 1990s. In particular, principles from robust control theory have been used by economic decision makers to investigate the fragility of decision rules across a range of economic models. In line with this tendency, our article applies principles from robustness to a situation where the decision maker is a bank owner and the decision rule determines the optimal provisioning strategy for loan losses. In this regard, we recognize that bank provisions are made for debts that have been identified as impaired or non-performing. Our first objective is to formulate a dynamic banking loan loss model involving a provisioning portfolio consisting of provisions for expected losses and loan loss reserves for unexpected losses. Here, unexpected loan losses and provisioning for expected losses are modeled via a compound Poisson process and an exponential Lévy process, respectively. Historical evidence from Organization for Economic Corporation and Development countries assists in confirming some of the modeling choices made. This setup naturally leads to a finite-horizon provisioning problem that may be solved via a mixed optimal/robust control approach involving a constraint for risk. Our investigation concludes with a brief analysis of some of the robustness issues and suggestions for topics of possible future research.