Controlled McKean–Vlasov Contagion with State-Dependent Killing

Battle Count: 72

The paper is primarily a theoretical contribution to stochastic analysis and optimal control in the context of systemic financial risk. It is relevant to quantitative risk management (systemic contagion modeling, regulatory intervention design, tail-risk assessment) rather than to direct trading strategy development. The HJB feedback control framework could inform dynamic hedging or portfolio rebalancing under contagion risk, but the paper does not address asset pricing, return prediction, or execution optimization. The multi-population contagion model with common noise is applicable to understanding correlated defaults in credit portfolios.

Extremely high complexity. The theoretical framework requires mastery of Wasserstein space calculus, Lions derivatives, viscosity solution theory on infinite-dimensional spaces, Poisson thinning constructions, and empirical process theory. The numerical HJB implementation involves 4-dimensional backward induction with semi-implicit diffusion steps, explicit common-noise cross terms, and semi-Lagrangian killing jumps. The synchronous coupling proofs span multiple lemmas with Gronwall-type estimates. Even the numerical validation requires careful grid calibration and Richardson extrapolation diagnostics.

Code is publicly available on GitHub with forward simulation, HJB feedback, and figure generation scripts. Calibration parameters (kill-intensity multiplier 25, terminal-loss weight 6, running-cost multiplier 0.05) are explicitly stated. Software versions (Python 3.12.7, NumPy 1.26.4, SciPy 1.13.1) are documented. However, the paper is primarily theoretical with proofs spanning 30+ pages, making full reproduction of analytical results non-trivial. Numerical experiments are reproducible but the HJB discretization diagnostics show sensitivity to grid resolution.