Optimal Loss Allocation in a Mean-Field Model of Systemic Risk

Battle Count: 85

The paper is primarily about systemic risk regulation and loss allocation policy, not about trading strategies or market microstructure. However, understanding systemic risk dynamics and default contagion mechanisms is relevant for risk management in trading portfolios, counterparty risk assessment, and stress testing. The mathematical tools (mean-field control, free boundary problems) have indirect connections to optimal execution and portfolio risk management, but the paper does not address any trading-specific problems.

This is a highly theoretical paper requiring advanced knowledge of stochastic analysis, mean-field control theory, viscosity solutions on Wasserstein space, free boundary problems, Skorokhod reflection, stochastic dominance theory, and dynamic programming. There is no computational implementation described. The mathematical machinery involves PDEs on infinite-dimensional spaces, singular controls, and convergence proofs in Skorokhod topology. Any numerical implementation would require solving coupled free-boundary PDEs and Hamilton-Jacobi equations on Wasserstein space, which is extremely challenging.

This is a pure theoretical mathematics paper with complete proofs of all theorems, lemmas, and propositions. All mathematical arguments are self-contained within the paper. No empirical data or code is needed. Reproducibility depends on verifying the mathematical proofs, which are fully provided. The companion work [14] on the comparison principle is referenced but not included.