Robust Optimal Portfolio and Bank Capital Adequacy Management

Abstract

The task of jointly estimating an optimal portfolio and bank capital adequacy ratio under model uncertainties is a real and challenging problem to portfolio managers in the banking industry. In this paper, we investigate the problem of optimal portfolio choice of an ambiguity averse portfolio manager (AAPM) with an obligation to continuously meet her bank’s capital adequacy requirements as specified in the BASEL III banking agreement. This is carried out through a stochastic modelling approach,requiringmodelspecificationuncertaintiesonthreecategoriesofabank’s balance sheet items-assets, capital and liabilities processes driven by independent Brownian motions. We prove the dynamic programming principle and derive the corresponding Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, leading to a robust capital adequacy ratio and an optimal portfolio selection. We conclude by looking at some numerical applications