ERM in an Optimal Control Framework

Much of ERM consists of qualitative discussion of the risks facing a business and controls over them. It is difficult to identify in the literature a clear body of theory to provide the foundation for the subject, integrating a business’s objectives with its risk controls.The present paper attempts this by formulation of ERM as an exercise in stochastic optimal control theory. Here there is a defined objective, which would usually include some aspect of profit, and a set of constraints (the risk controls). Optimal control theory provides a framework for balancing the one against the other, and also for considering whether or not particular risk controls are well advised.The paper accepts the COSO (2004) definition of ERM, and its associated ERM Integrated Framework. After definitions, preliminary discussion and establishment of the control theory set-up, the paper is organised with one section for each item of the ERM Integrated Framework. Each of these sections interprets that item within the control theory model.Risk controls may improve business performance, but they usually come at a cost. And the stronger the control, the greater may be the improvement, but the greater the cost. The essential purpose of the control theoretic formulation is the identification of the optimal strength of each risk control as that at which, for marginal further strengthening, the marginal improvement of business function is matched by marginal cost.