Contagious McKean–Vlasov systems with heterogeneous impact and exposure

Zachary Feinstein and Andreas Sojmark

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

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.

Keywords: mean-field limit; contagion; heterogeneous network; default cascades; dynamic interbank model; systemic risk (search for similar items in EconPapers)
JEL-codes: G21 G32 (search for similar items in EconPapers)
Pages: 49 pages
Date: 2023-07-01
New Economics Papers: this item is included in nep-ban and nep-net
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Finance and Stochastics, 1, July, 2023, 27(3), pp. 663 - 711. ISSN: 0949-2984

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:119457

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