论文标题
系统性鲁棒性：平均场粒子系统方法
Systemic robustness: a mean-field particle system approach
论文作者
论文摘要
本文关注的是，在涉及打击时间的随机微分方程模型的大粒子系统中，预算控制问题是由区域金融网络中系统性风险的考虑而产生的。由Tang和Tsai（Ann。probab。，46（2018），第1597页{1650）的动机，我们重点关注从未默认估算系统性鲁棒性的幸存实体的数量或比例。首先，我们表明，平均场粒子系统及其限制McKean-Vlasov方程都可以通过最小溶液的概念来良好。然后，我们建立了大粒子系统中幸存实体的比例与限制麦基vlasov方程中违约的概率之间的联系，因为相互作用的粒子系统的大小趋向于无穷大。最后，我们研究了不同经济体制中预算控制的渐近效率：在负面经济中，尚存实体的预期数量始终是秩序；它是中立经济中N的平方根的顺序。在预算的效果可以忽略不计的积极经济中，这是n的秩序。
This paper is concerned with the problem of budget control in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a regional financial network. Motivated by Tang and Tsai (Ann. Probab., 46(2018), pp. 1597{1650), we focus on the number or proportion of surviving entities that never default to measure the systemic robustness. First we show that both the mean-field particle system and its limiting McKean-Vlasov equation are well-posed by virtue of the notion of minimal solutions. We then establish a connection between the proportion of surviving entities in the large particle system and the probability of default in the limiting McKean-Vlasov equation as the size of the interacting particle system N tends to infinity. Finally, we study the asymptotic efficiency of budget control in different economy regimes: the expected number of surviving entities is of constant order in a negative economy; it is of order of the square root of N in a neutral economy; and it is of order N in a positive economy where the budget's effect is negligible.
