英文标题：
《A risk analysis for a system stabilized by a central agent》
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作者：
Josselin Garnier, George Papanicolaou, Tzu-Wei Yang
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最新提交年份：
2015
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英文摘要：
  We formulate and analyze a multi-agent model for the evolution of individual and systemic risk in which the local agents interact with each other through a central agent who, in turn, is influenced by the mean field of the local agents. The central agent is stabilized by a bistable potential, the only stabilizing force in the system. The local agents derive their stability only from the central agent. In the mean field limit of a large number of local agents we show that the systemic risk decreases when the strength of the interaction of the local agents with the central agent increases. This means that the probability of transition from one of the two stable quasi-equilibria to the other one decreases. We also show that the systemic risk increases when the strength of the interaction of the central agent with the mean field of the local agents increases. Following the financial interpretation of such models and their behavior given in our previous paper (Garnier, Papanicolaou and Yang, SIAM J. Fin. Math. 4, 2013, 151-184), we may interpret the results of this paper in the following way. From the point of view of systemic risk, and while keeping the perceived risk of the local agents approximately constant, it is better to strengthen the interaction of the local agents with the central agent than the other way around.
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中文摘要：
我们为个体和系统风险的演化建立并分析了一个多代理模型，其中本地代理通过一个中央代理相互作用，而中央代理又受本地代理的平均场的影响。中央代理由双稳态势稳定，这是系统中唯一的稳定力。局部代理仅从中心代理获得其稳定性。在大量本地代理的平均场极限中，我们表明，当本地代理与中央代理的交互强度增加时，系统风险降低。这意味着从两个稳定准平衡中的一个过渡到另一个的概率降低。我们还表明，当中央代理与本地代理的平均场的相互作用强度增加时，系统风险增加。根据我们之前论文（Garnier，Papanicolaou and Yang，SIAM J.Fin.Math.42001151-184）中给出的对此类模型及其行为的财务解释，我们可以用以下方式解释本文的结果。从系统性风险的角度来看，在保持本地代理的感知风险大致不变的同时，加强本地代理与中央代理之间的互动比反过来更好。
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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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