Systemic Risk and Stochastic Games with Delay

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

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arXiv · 1607.06373

Systemic Risk and Stochastic Games with Delay

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

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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 $N$ 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.

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BibTeX RIS

Rene Carmona, Jean-Pierre Fouque, Seyyed Mostafa Mousavi, Li-Hsien Sun. 2016-07-21. Systemic Risk and Stochastic Games with Delay. https://arxiv.org/abs/1607.06373

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