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At the mercy of the common noise: blow-ups in a conditional McKean–Vlasov Problem

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  • Ledger, Sean
  • Søjmark, Andreas

Abstract

We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to ‘blow-up’ phenomena whereby solutions develop jump-discontinuities. Our main results are twofold and concern the conditional McKean–Vlasov formulation of the model. First and foremost, we show that there are global solutions to this McKean–Vlasov problem, which can be realised as limit points of a motivating particle system with common noise. Furthermore, we derive results on the occurrence of blow-ups, thereby showing how these events can be triggered or prevented by the pathwise realisations of the common noise.

Suggested Citation

  • Ledger, Sean & Søjmark, Andreas, 2021. "At the mercy of the common noise: blow-ups in a conditional McKean–Vlasov Problem," LSE Research Online Documents on Economics 123787, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:123787
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    Cited by:

    1. Feinstein, Zachary & Sojmark, Andreas, 2021. "Short communication: dynamic default contagion in heterogeneous interbank systems," LSE Research Online Documents on Economics 123789, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    blow-ups; common noise; contagion; McKean–Vlasov problem; particle system; convergence;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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