Systemic Risk and Stochastic Games with Delay

René Carmona, Jean Pierre Fouque, Seyyed Mostafa Mousavi, Li Hsien Sun

研究成果: 雜誌貢獻期刊論文同行評審

12 引文 斯高帕斯(Scopus)

摘要

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.

原文???core.languages.en_GB???
頁(從 - 到)366-399
頁數34
期刊Journal of Optimization Theory and Applications
179
發行號2
DOIs
出版狀態已出版 - 1 11月 2018

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