Uniqueness for contagious McKean--Vlasov systems in the weak feedback regime

Autor:	Ledger, Sean, Sojmark, Andreas
Rok vydání:	2018
Předmět:	Mathematics - Probability Mathematics - Analysis of PDEs Quantitative Finance - Mathematical Finance 60H30 60G57 82C22 34B16 91G80
Druh dokumentu:	Working Paper
DOI:	10.1112/blms.12337
Popis:	We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random drivers. By weak feedback we mean the case where the contagion parameters are small enough to prevent blow-ups in solutions. Next, we specialise to a Brownian driver and show how the same techniques can be extended to give short-time uniqueness after blow-ups, regardless of the feedback strength. The heart of our approach is a surprisingly simple probabilistic comparison argument that is robust in the sense that it does not ask for any regularity of the solutions. Comment: 20 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.12356 Zobrazit plný text záznamu View this record from Arxiv