Controlled McKean--Vlasov Contagion with State-Dependent Killing

Abstract

We study controlled McKean--Vlasov contagion with state-dependent killing, common noise, loss feedback, and interacting populations. The main result is a comparison principle for the two-population killed-particle HJB on a decomposed state space of alive sub-probability measures and cemetery masses. The proof combines a Wasserstein smooth-gauge comparison argument with a killing-jump absorption estimate for mass transfer into the cemetery state. We also establish a multi-population mean-field limit, an explicit first-order particle convergence rate, conditional propagation of chaos, controlled well-posedness, and a steep-killing bridge to absorbing-boundary default. Finite-particle convergence tests and a two-population HJB feedback experiment illustrate the theory.