Balancing Shareholder Value and Financial Stability under a Reduced-Form Liquidation Model

2026-06-26

AI Summary

This study addresses the tension between shareholder value maximization and financial stability under a progressive, state-dependent bankruptcy resolution mechanism. By constructing a diffusion model partitioned into unregulated, regulated, and distress zones, and imposing a liquidation hazard rate that increases as surplus declines, the authors formulate and solve a singular stochastic control problem aimed at maximizing the present value of shareholder dividends. They establish the optimality of a barrier-type policy and demonstrate that introducing a distress zone solely above or below the classical ruin threshold fails to simultaneously enhance both shareholder value and firm survival probability, whereas a hybrid design achieves a Pareto improvement. Leveraging a reduced-form liquidation framework and diffusion analysis, they derive closed-form expressions for the value function and expected survival time, providing an efficient tool for comparing alternative regulatory architectures and underscoring the pivotal role of regulatory design in balancing these dual objectives.

Abstract

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.

Problem

• shareholder value
• financial stability
• liquidation
• regulatory design
• distressed firms

Innovation

• reduced-form liquidation
• singular stochastic control
• barrier strategy
• financial stability
• state-dependent regulation