This thesis consists of two essays concerning how banking regulations may promote financial stability. The first chapter investigates the competition-concentration-stability nexus from a novel perspective, by considering how concentration and, inter alia competition, affect the likelihood of an individual bank failing, and the likelihood of the bank failure spreading contagiously to the rest of the banking system. Competition is shown to reduce individual bank and systemic stability by reducing banks' profit buffers to absorb liquidity shocks. The impact of concentration on stability is more nuanced however, as increased concentration increases banks' profit buffers but also increases the concentration risk in the interbank market, widening the channel of contagion by which a liquidity shock can spread throughout the network. The second chapter concerns optimal ex-ante prudential regulation and ex-post resolution policy of globally systemically important banks. It characterises the conditions under which weakly capitalised, limitedly liable banks have incentives to 'gamble for resurrection' by investing in risky asset portfolios, in the knowledge that the downside risk is shifted onto the deposit insurance fund. In this context it is shown that a bank resolution by `bailing in' unsecured debt holders can restore the incentive for banks to act prudently, and that the bail-in should occur above the point of insolvency to ensure the bank has sufficient skin in the game. The interplay of three ex-ante prudential regulatory instruments is analysed: the minimum capital and total loss absorbing capacity requirements and the minimum capital buffer. The minimum capital and TLAC requirements are set to ensure that the bank has sufficient skin in the game to invest prudently and tradeoff the ex-post costs of bailing in unsecured debt holders, the cost of bailing out depositors and the cost of equity issuance, and minimum equity buffer is set to ensure an appropriate trigger for resolution.