Robust Optimal Portfolio and Bank Capital Adequacy Management

Abstract

The joint task of optimal portfolio selection and bank capital adequacy management is a real and challenging problem to portfolio managers in the banking industry. In this work, we investigate the problem of optimal portfolio choice of an ambiguity averse portfolio manager (AAPM) with an obligation to continuously meet her/his bank’s capital adequacy requirements as specified in the BASEL III Banking Agreement. Such a problem deals with the non-linear stochastic optimal control problem whose solution is determined by means of the dynamic programming principle applied to corresponding Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation. The analysis relies heavily on the stochastic modelling requiring a robust portfolio optimization approach on three categories of a bank’s balance sheet items: assets, capital and liabilities. We modelled the ambiguity by means of classical dynamic programming principle and the non-linear expectation. We showed that modelling ambiguity via the classical optimal portfolio and by the Choquet expectation have completely different impacts on portfolio selection and the capital adequacy ratio by comparing the utility losses. We explored the effects of ambiguity on optimal portfolio choice and capital adequacy and demonstrated that the ambiguity aversion level decreases the optimal proportions of the risky assets while the Choquet capacity increases them. We considered the portfolio manager who wishes to maximize the expected utility of terminal wealth where only the price of the assets are available but the ambiguity parameter in the market is not observable. We used the Kalman filtering method to convert the partial information given by the observable portfolio asset and the unobservable uncertainty parameter to a full information problem. We then obtained the HJB equation of the resulting full information. We concluded that the conditional Choquet expectation gives the more realistic assumption in the derivation of the robust portfolio selection and capital adequacy.