英文标题：
《Systemic Risk and Heterogeneous Mean Field Type Interbank Network》
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作者：
Li-Hsien Sun
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最新提交年份：
2019
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英文摘要：
  We study the system of heterogeneous interbank lending and borrowing based on the relative average of log-capitalization given by the linear combination of the average within groups and the ensemble average and describe the evolution of log-capitalization by a system of coupled diffusions. The model incorporates a game feature with homogeneity within groups and heterogeneity between groups where banks search for the optimal lending or borrowing strategies through minimizing the heterogeneous linear quadratic costs in order to avoid to approach the default barrier. Due to the complicity of the lending and borrowing system, the closed-loop Nash equilibria and the open-loop Nash equilibria are both driven by the coupled Riccati equations. The existence of the equilibria in the two-group case where the number of banks are sufficiently large is guaranteed by the solvability for the coupled Riccati equations as the number of banks goes to infinity in each group. The equilibria are consisted of the mean-reverting term identical to the one group game and the group average owing to heterogeneity. In addition, the corresponding heterogeneous mean filed game with the arbitrary number of groups is also discussed. The existence of the $\\epsilon$-Nash equilibrium in the general $d$ heterogeneous groups is also verified. Finally, in the financial implication, we observe the Nash equilibria governed by the mean-reverting term and the linear combination of the ensemble averages of individual groups and study the influence of the relative parameters on the liquidity rate through the numerical analysis.
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中文摘要：
我们研究了基于组内平均数和集合平均数线性组合得出的对数资本化相对平均数的异质银行间借贷系统，并通过耦合扩散系统描述了对数资本化的演化。该模型结合了集团内部同质性和集团之间异质性的博弈特征，其中银行通过最小化异质线性二次成本来寻求最优借贷策略，以避免接近违约壁垒。由于借贷系统的复杂性，闭环纳什均衡和开环纳什均衡均由耦合的Riccati方程驱动。当两组中的组数趋于无穷大时，耦合Riccati方程的可解性保证了平衡点在组数足够大的两组情况下的存在性。均衡由与一组博弈相同的均值回复项和由于异质性导致的组平均值组成。此外，还讨论了相应的任意群数的异质平均场对策。还验证了一般$d$异质群中$\\ε$-纳什均衡的存在性。最后，在金融含义中，我们观察了由均值回复项和各群体集合平均数的线性组合所控制的纳什均衡，并通过数值分析研究了相关参数对流动性比率的影响。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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