An optimization approach to the dynamic allocation of economic capital

We propose an optimization approach to allocating economic capital, distinguishing between an allocation or raising principle and a measure for the risk residual. The approach is applied both at the aggregate (conglomerate) level and at the individual (subsidiary) level and yields an integrated solution to the capital allocation problem. In particular, we formalize a procedure to determine (i) the optimal amount of economic capital to be held by a financial conglomerate, (ii) the optimal allocation of this amount among the subsidiaries and (iii) a consistent distribution of the cost of risk-bearing borne by the conglomerate. Different degrees of information on the dependence structure between the subsidiaries are considered. The results provide a theoretical justification for the use of Value-at-Risk, not as a measure of risk, but as an optimal allocation or raising principle. Static solutions are generalized to a dynamic setting. The approach is illustrated using an example of a financial conglomerate represented by a multivariate Wiener process.