Capital adequacy management for banks in the Lévy market

Ponente(s): Muhammad Kashif .

We investigate the capital adequacy management and asset allocation problems for a bank whose risk process follows a jump-diffusion process. Capital adequacy management problem is based on regulations in Basel III Capital Accord such as the capital adequacy ratio (CAR) which is calculated by the dividing the bank capital by total risk-weighted assets (TRWAs). Capital adequacy management requires a bank to reserve a certain amount for liquidity. We derive the optimal investment portfolio for a bank with constant absolute risk aversion (CARA) preferences and then the capital adequacy ratio process of the bank is derived, conditional on the optimal policy chosen. We address the optimal portfolio selection problem incorporating the bank’s risk process using the martingale approach. We first solve the asset allocation problem and then the capital adequacy ratio process of the bank is derived, conditional on the optimal policy chosen. In comparison with the Merton’s approach, we add a jump diffusion process in the stock that is simultaneous to the jump in the bank’s risk process modeled by Cramer-Lundberg model. Furthermore, we have used a jump process to model the expected losses that covered the loan loss provision.