Particle systems with singular interaction through hitting times: Application in systemic risk modeling
Particle systems with singular interaction through hitting times: Application in systemic risk modeling
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DOI：
10.1214/18-aap1403
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
S. Nadtochiy;Mykhaylo Shkolnikov
中科院分区：
文献类型：
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作者：
S. Nadtochiy;Mykhaylo Shkolnikov
我们提出了一个相互作用的粒子系统来模拟具有相互风险敞口的银行系统的演化。在该模型中，当一家银行的正常化资产价值达到较低门槛时，它就会违约，而它的违约会给其他银行带来即时损失，可能会引发一连串的违约。这种相互作用的强度取决于所谓的非核心暴露的水平。我们发现，当系统规模变大时，一家银行因其他银行违约而产生的累积损失过程表现出不连续性。这些不连续性自然被解读为系统性事件，我们根据非核心风险敞口的水平和即将违约的银行比例来明确描述这些事件。我们工作的主要数学挑战来自于粒子之间相互作用的非常独特的性质，这是由限制系统继承的。在[DIRT15a]和[DIRT15b]中分析了一个类似的粒子系统，我们在他们结果的基础上进行了改进和推广。特别地，我们刻画了系统的大种群极限，分析了跳跃次数、跳跃之间的规律性以及极限过程的局部唯一性。
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other banks, possibly triggering a cascade of defaults. The strength of this interaction is determined by the level of the so-called non-core exposure. We show that, when the size of the system becomes large, the cumulative loss process of a bank resulting from the defaults of other banks exhibits discontinuities. These discontinuities are naturally interpreted as systemic events, and we characterize them explicitly in terms of the level of non-core exposure and the fraction of banks that are "about to default". The main mathematical challenges of our work stem from the very singular nature of the interaction between the particles, which is inherited by the limiting system. A similar particle system is analyzed in [DIRT15a] and [DIRT15b], and we build on and extend their results. In particular, we characterize the large-population limit of the system and analyze the jump times, the regularity between jumps, and the local uniqueness of the limiting process.