Work

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

Year: 2020

Type: article

Abstract: 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, by exploiting a localised form of weak feedback. 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.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.12337

Authors: Sean Ledger, Andreas Søjmark

Institutions: University of Bristol, Imperial College London

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: EPSRC Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications