Tractable bank capital structure: optimal control under Basel III constraints

Paper: arXiv 2603.14557

Authors: Erhan Bayraktar, Etienne Chevalier, Vathana Ly Vath, Yuqiong Wang

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using stochastic control to reduce high-dimensional balance sheet dynamics into a tractable one-dimensional model under Basel III constraints. While the mathematical derivation and optimization of dividend/recapitalization thresholds are highly sophisticated, empirical validation relies primarily on Monte Carlo simulations rather than historical backtesting or empirical market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Optimize bank capital structure & policy under Basel III constraints] --> B[Model Balance Sheet & Constraints:<br/>Solvency, Liquidity, & Costly Equity Issuance]
    B --> C[Dimensionality Reduction:<br/>Map dynamic system to 1D Leverage Ratio]
    C --> D[Stochastic Control Optimization:<br/>Derive analytical threshold policies]
    D --> E[Outer Optimization & Monte Carlo:<br/>Map Shareholder Value vs. Survival Trade-off]
    E --> F[Findings: Target recapitalization boundary,<br/>dividend reflection barrier, & optimal solvency caps]

Cited References (36)

1. Basel III : The Liquidity Coverage Ratio and liquidity risk monitoring tools (2013) — link
2. Basel III leverage ratio framework - Executive summary (2017) — link
3. A Class of Singular Stochastic Control Problems with Optimal Stopping and Impulse Control (2008) — link
4. Liquidity risk and optimal dividend/investment strategies (2017) — link
5. An optimal dividend and investment control problem under debt constraints (2013) — link
6. A diffusion model for optimal dividend distribution for a company with constraints on risk control (2003) — link
7. User’s guide to viscosity solutions of second order partial differential equations (1992) — link
8. Optimal dividend policy and growth option (2007) — link

0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.