Systemic Risk and Stochastic Games with Delay

Rene Carmona, Jean-Pierre Fouque, Seyyed Mostafa Mousavi and Li-Hsien Sun

Papers from arXiv.org

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 $N$ 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 an $N$-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 close-loop Nash equilibrium using an HJB approach.

Date: 2016-07
New Economics Papers: this item is included in nep-gth and nep-hpe
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Citations: View citations in EconPapers (5)

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