Systemic Risk and Stochastic Games with Delay

René Carmona (), Jean-Pierre Fouque (), Seyyed Mostafa Mousavi () and Li-Hsien Sun ()
Additional contact information
René Carmona: Princeton University
Jean-Pierre Fouque: University of California Santa Barbara
Seyyed Mostafa Mousavi: University of California Santa Barbara
Li-Hsien Sun: National Central University

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 2, No 2, 366-399

Abstract: Abstract We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into account a quadratic cost for lending or borrowing and a linear incentive to borrow if the reserve is low or lend if the reserve is high relative to the average capitalization of the system. As such, our problem is a finite-player linear–quadratic stochastic differential game with delay. An open-loop Nash equilibrium is obtained using a system of fully coupled forward and advanced-backward stochastic differential equations. We then describe how the delay affects liquidity and systemic risk characterized by a large number of defaults. We also derive a closed-loop Nash equilibrium using a Hamilton–Jacobi–Bellman partial differential equation approach.

Keywords: Systemic risk; Inter-bank borrowing and lending; Stochastic game with delay; Nash equilibrium; 91A15; 91G80; 60G99 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (23)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1267-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-018-1267-8

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-1267-8

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().