Tractable bank capital structure: optimal control under Basel III constraints

2026-03-15

AI Summary

This study investigates how banks optimally coordinate risk-taking, dividend payouts, and capital structure under Basel III capital and liquidity constraints, with a focus on efficiently deploying costly equity financing for post-crisis recovery. By reducing the high-dimensional balance sheet dynamics to a one-dimensional stochastic control problem in terms of the leverage ratio and incorporating a state-dependent investment cap, the paper constructs—for the first time—an analytically tractable dual-threshold reflected boundary policy that jointly governs optimal dividend distribution and recapitalization. This policy possesses clear economic interpretation, delineating an efficient frontier between shareholder value and survival probability. The analysis demonstrates that strengthening solvency regulation—particularly through imposing a leverage ratio ceiling—achieves an optimal trade-off between safety and profitability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Coordination and Collaboration
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Basel III
• bank capital structure
• stochastic control
• solvency constraints
• leverage ratio

Innovation

• stochastic control
• leverage ratio
• Basel III constraints
• optimal recapitalization
• reflection barrier