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

Sean Ledger and Andreas Søjmark

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: blow-ups; common noise; contagion; McKean–Vlasov problem; particle system; convergence (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2021-03-23
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Electronic Journal of Probability, 23, March, 2021, 26(none). ISSN: 1083-6489

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:123787

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