Stochastic modelling in bank management and optimization of bank asset allocation

Abstract

The Basel Committee published its proposals for a revised capital adequacy framework(the Basel II Capital Accord) in June 2006. One of the main objectives of this framework is to improve the incentives for state-of-the-art risk management in banking, especially in the area of credit risk in view of Basel II. The new regulation seeks to provide incentives for greater awareness of differences in risk through more risk-sensitive minimum capital requirements based on numerical formulas. This attempt to control bank behaviour has a heavy reliance on regulatory ratios like the risk-based capital adequacy ratio (CAR). In essence, such ratios compare the capital that a bank holds to the level of credit, market and operational risk that it bears. Due to this fact the objectives in this dissertation are as follows. Firstly, in an attempt to address these problems and under assumptions about retained earnings, loan-loss reserves, the market and shareholder-bank owner relationships, we construct continuous-time models of the risk-based CAR which is computed from credit and market risk-weighted assets (RWAs) and bank regulatory capital (BRC) in a stochastic setting. Secondly, we demonstrate how the CAR can be optimized in terms of equity allocation. Here, we employ dynamic programming for stochastic optimization, to obtain and verify the results. Thirdly, an important feature of this study is that we apply the mean-variance approach to obtain an optimal strategy that diversifies a portfolio consisting of three assets. In particular, chapter 5 is an original piece of work by the author of this dissertation where we demonstrate how to employ a mean-variance optimization approach to equity allocation under certain conditions.