论文标题
具有默认和恢复的大型银行系统：平均现场游戏模型
Large Banking Systems with Default and Recovery: A Mean Field Game Model
论文作者
论文摘要
我们考虑了大型银行系统的平均模型，该模型考虑了机构的默认和恢复。在用于相互作用神经元组的模型的基础上，我们首先研究了McKean-Vlasov动力学及其进化的Fokker-Planck方程，其中均值场相互作用通过均值转移项以及对应于默认水平的命中时间进行。后一个功能反映了金融机构违约对银行系统储量全球分配的影响。金融机构的系统性风险问题被理解为Fokker-Planck方程的爆炸现象。然后，我们通过让机构控制其动力学的一部分，以最大程度地降低其预期风险，从而在模型中纳入优化组件。将此优化问题措辞作为平均场游戏，我们在特殊情况下提供了一个明确的解决方案，在一般情况下，我们根据有限差异方案报告了数值实验。
We consider a mean-field model for large banking systems, which takes into account default and recovery of the institutions. Building on models used for groups of interacting neurons, we first study a McKean-Vlasov dynamics and its evolutionary Fokker-Planck equation in which the mean-field interactions occur through a mean-reverting term and through a hitting time corresponding to a default level. The latter feature reflects the impact of a financial institution's default on the global distribution of reserves in the banking system. The systemic risk problem of financial institutions is understood as a blow-up phenomenon of the Fokker-Planck equation. Then, we incorporate in the model an optimization component by letting the institutions control part of their dynamics in order to minimize their expected risk. Phrasing this optimization problem as a mean-field game, we provide an explicit solution in a special case and, in the general case, we report numerical experiments based on a finite difference scheme.
