  We formulate banks' capital optimization problem as a classic mean variance
optimization, by leveraging an accurate linear approximation to the Shapely or
Constrained Aumann-Shapley (CAS) allocation of max or nested max cost
functions. This reduced form formulation admits an analytical solution, to the
optimal leveraged balance sheet (LBS) and risk weighted assets (RWA) target of
banks' business units for achieving the best return on capital.
