Modern resolution and prudential regimes increasingly wind up a distressed firm not at a single hard threshold but through a graduated, state-dependent process. We study how the design of such a regime shapes the trade-off between shareholder value and financial stability for a firm whose surplus follows a general diffusion. Forced liquidation is modelled in reduced form, arriving at a surplus-dependent hazard rate that rises as the firm's position deteriorates. The framework has three regions: an unregulated region where dividends may be paid, a regulated region where solvency requirements prohibit distributions, and a distress region in which the firm faces the liquidation hazard. To quantify shareholder value we solve the resulting singular stochastic control problem: which is to maximise the expected present value of distributions until liquidation. We establish a verification theorem, prove that a barrier strategy is optimal, and obtain tractable expressions for the value function and the expected survival time, so that alternative designs can be compared at low cost. We show that a distress region placed solely below or solely above the classical ruin threshold does not consistently improve both shareholder value and firm survival, whereas combining the two yields a Pareto improvement. Regulatory design is decisive.
We propose a novel valuation framework for contingent convertible (CoCo) bonds based on the issuing bank's Common Equity Tier 1 (CET1) ratio, which is widely acknowledged as an indicator of a bank's solvency. Our approach develops a bivariate jump-diffusion model that captures the dynamic relationship linking the CET1 ratios, share prices, and CoCo bond prices, incorporating both continuous market movements and correlated jump risk. The model advances existing literature through three key innovations: (1) a hybrid mechanism for modeling regulatory discretion in trigger decisions, (2) a class of power conversion schemes that generalizes traditional approaches while maintaining analytical tractability, and (3) a method to overcome the temporal discrepancy between high-frequency market data and low-frequency regulatory reporting. We derive semi-closed form formulas for both write-down and equity-convertible CoCo bonds and validate our model through five case studies spanning from 2009 to 2023, including an in-depth analysis of the 2023 Credit Suisse collapse. The results demonstrate a significant improvement in pricing and hedging performance while highlighting the model's data-adaptive nature that enables short-term predictions.
We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead to endogenous insolvency. By incorporating Basel III regulatory requirements (LCR and NSFR) into a stochastic optimal control framework, we solve for the exact insolvency boundary using the Hamilton-Jacobi-Bellman (HJB) equation. To bridge the gap between theoretical complexity and supervisory practice, we derive and validate a surrogate analytical approximation function that allows for real-time monitoring. Calibrated using granular balance-sheet data from the Iranian banking sector, our model reveals significant non-linear threshold effects: the joint occurrence of liquidity stress and credit portfolio defaults disproportionately accelerates the transition toward insolvency compared to their individual effects. The proposed surrogate function offers supervisors a computationally efficient tool for stress testing and early warning systems. Our findings provide novel insights into financial frictions in emerging markets and offer a rigorous framework for integrated risk management.
We develop a rigorous framework for modeling collateral liquidations in decentralized lending protocols such as Aave and Compound. In contrast to earlier approaches based on constant-product market maker (CPM) assumptions, real-world liquidations are executed through order books with finite depth. This introduces price impact, modifies solvency conditions, and reduces safe loan-to-value ratios. We introduce the Aggregate Value Function, defined directly on the order book, and establish its monotonicity, concavity, and quasi-linearity, following the quasi-linear order book framework. Building on these properties, we derive solvency inequalities and explicit formulas for safe leverage. Our model extends CPM-based theory to discrete liquidity environments and provides foundations for risk management and parameter design in lending protocols.
Matvii Tulupov· Theoretical and Applied Cybe...· 0 citations
This article studies a dynamic corporate risk management problem by considering the decision-making of risk-averse managers who exert costly effort and select project risk. We study how a Value-at-Risk (VaR) constraint affects managerial decisions and the distribution of firm value when the manager's objective is non-concave with a fixed salary and options. By the concavification technique, we analyze the optimal terminal firm value on the concave envelope of the objective function. Applying the quantile formulation and the martingale approach, we can derive explicit solutions for optimal effort, terminal firm value, and project choice. The optimal terminal firm value can be divided into nine cases by carefully discussing the choices of VaR floor and tail probability. Compared with the benchmark case, we find that a VaR manager will smooth terminal firm value across states, reducing it in good states while supporting it in adverse states. Moreover, a VaR requirement generally improves downside protection and reduces bankruptcy probability when the VaR floor is low or moderate. However, when the VaR floor is sufficiently high, it can increase bankruptcy probability and induce gambling-for-recovery behavior in adverse states. Our sensitivity analysis indicates that greater managerial effort uniformly improves firm value. Moreover, more incentive options make managers more responsible, leading to a smoother terminal firm value across states. In contrast, a high fixed salary makes the manager less responsible and ultimately causes a more dispersed firm value.
The Chinese A-share market, characterized by its unique retail-dominated structure and institutional constraints, exhibits pricing features distinct from mature markets. This study constructs a portfolio management framework adapted to the microstructure of the A-share market and examines how institutional investors can generate excess returns through Bubble Riding and Factor Timing strategies when limited arbitrage and investor irrationality coexist. First, using a synchronization-risk framework and a behavioral overreaction mechanism, we derive that the optimal strategy for rational arbitrageurs under heterogeneous beliefs and short-sale constraints can shift from immediate mean reversion to momentum-following. Subsequently, we integrate a China-localized factor construction and conduct an empirical study using A-share data from 2020 to 2026 collected through Python and the Baostock interface. The results show that: (1) traditional Fama-French factors are weakened in the A-share market when shell-value contamination is ignored, and excluding the bottom 30% of micro-cap stocks improves pricing efficiency; (2) momentum and sentiment factors exhibit nonlinear characteristics across market regimes; and (3) a dynamic risk-control strategy based on market-wide turnover rates—penalizing high-volatility exposure during bubble periods and increasing beta exposure during freezing periods—substantially outperforms the CSI 300 index out of sample.
Wensheng Yi, Zijian Zeng, Gao Ke et al.· Wseas Transactions on Busine...· 0 citations
This paper investigates the optimal design of information disclosure at debt rollover to maximize an entrepreneur’s ex ante borrowing capacity and social welfare. We develop a model where an entrepreneur secures a startup loan for project experimentation and must refinance for production. Borrowing capacity is limited by the pledgeability of project cash flows, which is eroded by three interacting forces: the entrepreneur’s moral hazard, premature liquidation risk following a liquidity shock, and rent dissipation arising from creditor competition. We show that a coarse “pass-or-fail” signal structure maximizes borrowing capacity. This binary structure is informative to balance incentive provision against liquidation risk, yet sufficiently coarse to mitigate rent dissipation. Furthermore, we demonstrate that the welfare-maximizing signal structure remains a pass-or-fail form, with an optimal threshold that tightens as the entrepreneur’s borrowing need increases.
This paper was accepted by Lin William Cong, finance.
Funding: H. Xu acknowledges support from the National Social Science Fund of China [Project Code: 23BJY251].
Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2024.07999 .