In the first part of the dissertation, we investigate the relationship between assets diversification and the probability of systemic default under Merton default models and first passage times models. Our study is based on continuous time log-normal models, which complements the works available in the literature most of which are based on one period discrete time models with assets following normal or uniform distributions. We find that a bank's degree of diversification may be higher than which is optimal for the stability of financial system, which motivate the need for diversification regulation.

In the second part of the dissertation, we study how banks respond to changing regulations. We propose a dynamic model with bank's asset and short term funding driven by Brownian motions. Under our model, the regulator impose capital requirement, liquidity coverage ratio and net stable funding requirement and the bank optimises its decisions to maximize equity holder's return subject to regulatory requirements. We discuss the cases where the bank behaves as expected by the regulators and cases where the regulations cannot achieve the goals as planned.