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Systemic Risk and Stochastic Games with Delay

Author(s): Carmona, Rene; Fouque, JP; Mousavi, SM; Sun, LH

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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.
Publication Date: 1-Nov-2018
Citation: Carmona, R, Fouque, JP, Mousavi, SM, Sun, LH. (2018). Systemic Risk and Stochastic Games with Delay. Journal of Optimization Theory and Applications, 179 (2), 366 - 399. doi:10.1007/s10957-018-1267-8
DOI: doi:10.1007/s10957-018-1267-8
ISSN: 0022-3239
EISSN: 1573-2878
Pages: 366 - 399
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Optimization Theory and Applications
Version: Author's manuscript

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