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Controlled McKean--Vlasov Contagion with State-Dependent Killing

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  • Aoxin Zhang
  • Yingzhe Wang

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.

Suggested Citation

  • Aoxin Zhang & Yingzhe Wang, 2026. "Controlled McKean--Vlasov Contagion with State-Dependent Killing," Papers 2605.24833, arXiv.org, revised Jun 2026.
    • Handle: RePEc:arx:papers:2605.24833
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