Dynamic Banking with Endogenous Risk Based Funding Cost: Value Maximization, Risk-taking, Responses to Regulation and Credit Contraction

We develop a stochastic dynamic model of bank value maximization under limited liability and in which bankruptcy can occur. Main issues are banks’ optimal responses to regulation and credit-losses. We show that risk-neutral banks behave as if they were risk-averse when they are under-capitalized. Risk-taking is always below that of single period value maximization under limited liability. We also show that banking regulations often have significant and adverse second-order effects through banks’ dynamic adjustment to regulations. The model gives rise to endogenous capital buffers and shows that it takes time to re-build bank capital after a credit-loss. That makes the model suitable to analysis of situations as the current post financial crisis period with large macroeconomic disturbances and credit contraction.