Basel II banking regulation introduces new needs for computational schemes. They involve both optimal stochastic control, and large scale simulations of decision processes of preventing low-frequency high loss-impact events. This paper will first state the problem and present its parameters. It then spells out the equations that represent a rational risk management behavior and link together the variables: Levy processes are used to model operational risk losses, where calibration by historical loss databases is possible ; where it is not the case, qualitative variables such as quality of business environment and internal controls can provide both costs-side and profits-side impacts. Among other control variables are business growth rate, and efficiency of risk mitigation. The economic value of a policy is maximized by resolving the resulting Hamilton-Jacobi-Bellman type equation. Computational complexity arises from embedded interactions between 3 levels: * Programming global optimal dynamic expenditures budget in Basel II context, * Arbitraging between the cost of risk-reduction policies (as measured by organizational qualitative scorecards and insurance buying) and the impact of incurred losses themselves. This implies modeling the efficiency of the process through which forward-looking measures of threats minimization, can actually reduce stochastic losses, * And optimal allocation according to profitability across subsidiaries and business lines. The paper next reviews the different types of approaches that can be envisaged in deriving a sound budgetary policy solution for operational risk management, based on this HJB equation. It is argued that while this complex, high dimensional problem can be resolved by taking some usual simplifications (Galerkin approach, imposing Merton form solutions, viscosity approach, ad hoc utility functions that provide closed form solutions, etc.) , the main interest of this model lies in exploring the scenarios in an adaptive learning framework ( MDP, partially observed MDP, Q-learning, neuro-dynamic programming, greedy algorithm, etc.). This makes more sense from a management point of view, and solutions are more easily communicated to, and accepted by, the operational level staff in banks through the explicit scenarios that can be derived. This kind of approach combines different computational techniques such as POMDP, stochastic control theory and learning algorithms under uncertainty and incomplete information. The paper concludes by presenting the benefits of such a consistent computational approach to managing budgets, as opposed to a policy of operational risk management made up from disconnected expenditures. Such consistency satisfies the qualifying criteria for banks to apply for the AMA (Advanced Measurement Approach) that will allow large economies of regulatory capital charge under Basel II Accord.
