Contagious McKean–Vlasov systems with heterogeneous impact and exposure

Feinstein, Zachary and Sojmark, Andreas ORCID: 0000-0001-7488-0221 (2023) Contagious McKean–Vlasov systems with heterogeneous impact and exposure. Finance and Stochastics, 27 (3). 663 - 711. ISSN 0949-2984

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Abstract

We introduce a particular heterogeneous formulation of a class of contagious McKean–Vlasov systems, whose inherent heterogeneity comes from asymmetric interactions with a natural and highly tractable structure. It is shown that this formulation characterises the limit points of a finite particle system, deriving from a balance-sheet-based model of solvency contagion in interbank markets, where banks have heterogeneous exposure to and impact on the distress within the system. We also provide a simple result on global uniqueness for the full problem with common noise under a smallness condition on the strength of interactions, and we show that in the problem without common noise, there is a unique differentiable solution up to an explosion time. Finally, we discuss an intuitive and consistent way of specifying how the system should jump to resolve an instability when the contagious pressures become too large. This is known to happen even in the homogeneous version of the problem, where jumps are specified by a ‘physical’ notion of solution, but no such notion currently exists for a heterogeneous formulation of the system.

Item Type:	Article
Additional Information:	© 2023 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management H Social Sciences > HG Finance
JEL classification:	G - Financial Economics > G2 - Financial Institutions and Services > G21 - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure
Date Deposited:	21 Jun 2023 13:30
Last Modified:	18 Nov 2024 18:09
URI:	http://eprints.lse.ac.uk/id/eprint/119457

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