Optimal asset allocation for a bank under risk control

Motivated by the Basel III requirement we analyze an optimal Capital Adequacy Ratio subject to foreclosure risk exposure. We assume that the banker invests in treasuries, a stock index and a loan portfolio, where he/she wishes to maximize his/her expected utility of terminal wealth by selecting optimal investment and risk control strategies. The dynamics of the stock index and the banker’s risk exposure towards foreclosure is modeled as two independent compensated pure jump Lévy Processes. By applying the martingale approach we obtain a closed form solution for this optimization problem under a quadratic utility function. A negative correlation between the banker’s foreclosure risk and the price dynamics of stock index will result in a reduced amount invested in stock index fund while a positive correlation between the banker’s foreclosure risk and the price dynamics of stock index will increase the amount invested in stock index fund.