Systemic Risk and Stochastic Games with Delay
Systemic Risk and Stochastic Games with Delay
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DOI：
10.1007/s10957-018-1267-8
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发表时间：
2018-03
影响因子：
1.9
通讯作者：
R. Carmona;J. Fouque;S. M. Mousavi;Li-Hsien Sun
中科院分区：
文献类型：
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作者：
R. Carmona;J. Fouque;S. M. Mousavi;Li-Hsien Sun
我们提出了一个考虑清算债务义务的银行间借贷模型。银行对数货币准备金的演化是由控制驱动的耦合扩散描述的，其漂移具有延迟。银行正在最小化其有限期限目标函数，该目标函数考虑了借贷的二次成本以及在准备金相对于系统平均资本化较低时借贷或在准备金相对于系统平均资本化较高时借贷的线性激励。因此，我们的问题是一个有限局中人线性二次随机微分对策与延迟。一个开环纳什均衡是使用一个系统的完全耦合的向前和先进的向后随机微分方程。然后，我们描述了延迟如何影响流动性和系统性风险的特点是大量的违约。我们还推导出一个闭环纳什均衡使用汉密尔顿-雅可比-贝尔曼偏微分方程的方法。
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.