A One-Step Neural FBSDE Solver for Mean-Field Sovereign Default Equilibria

摘要

We formulate world sovereign default as a high-dimensional equilibrium learning problem with distributional states, endogenous prices, and discontinuous default boundaries. In the model, a continuum of sovereign borrowers faces idiosyncratic and common risk, while a constrained intermediary prices sovereign debt and capital. The main computational difficulty is that default risk is determined by the local mass and composition of sovereigns near the default boundary, information that moment-based aggregate summaries can erase. We therefore use the conditional cross-sectional law of sovereigns and intermediary net worth as the aggregate state. We show that the resulting recursive equilibrium admits a probabilistic forward--backward representation coupling stochastic distributional dynamics, sovereign value equations, and intermediary marginal-value pricing. We then introduce a one-step actor--learner scheme: versioned continuation evaluators construct detached Backward Euler targets, and neural actor--critic maps learn the equilibrium fixed point. This provides a bridge between mean-field equilibrium computation, multi-agent reinforcement learning, and quantitative models with endogenous default.