Tractable bank capital structure: optimal control under Basel III constraints

Banks must optimize risky investments, dividend payouts, and capital structure under tight Basel III solvency and liquidity constraints, while costly equity issuance serves as a distress-recovery tool. We formulate this as a stochastic control problem that reduces the high-dimensional balance-sheet dynamics to a tractable one-dimensional process in the leverage ratio, with state-dependent investment limits. The resulting policy is simple and interpretable: pay dividends at an upper reflection barrier and, when needed, recapitalize only at the distress boundary, jumping to a unique target level. We characterize these thresholds analytically and show their sensitivity to regulatory parameters. From a regulatory viewpoint, we solve an outer optimization problem that maps the efficient frontier between shareholder value and survival probability (via Monte Carlo), with and without leverage caps. Results highlight that tightening solvency requirements often yields the best safety-profitability trade-off.