系统性风险度量的计算：一种混合整数规划方法
Computation of systemic risk measures: a mixed-integer programming approach
AI总结：
本文针对具有复杂清算机制的金融系统，提出基于混合整数规划的方法计算Rogers-Veraart网络模型扩展中的清算向量，并探讨了相应非凸向量优化问题的标量化理论及计算实例验证。
摘要：
系统性风险关注金融系统的不稳定性，其成员相互依赖，即少数机构的失败可能引发整个系统的连锁违约。近期文献提出了几种系统性风险度量，用于在联合风险考量下确定成员的资本要求。我们解决了具有复杂清算机制的系统的系统性风险度量计算问题。特别地，我们考虑了Rogers-Veraart网络模型的扩展，其中运营现金流符号不受限制。我们提出了一个混合整数规划问题，可用于计算该模型中的清算向量。由于该问题中存在二元变量，相应的（集值）系统性风险度量通常无法具有凸值。我们将非凸向量优化问题与系统性风险度量相关联，并提供了与该问题的加权和及Pascoletti-Serafini标量化相关的理论结果。最后，我们在计算实例上测试了所提出的公式，并针对一些模型特定和结构性参数进行了敏感性分析。
英文摘要：
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures have been proposed in the literature that are used to determine capital requirements for the members subject to joint risk considerations. We address the problem of computing systemic risk measures for systems with sophisticated clearing mechanisms. In particular, we consider an extension of the Rogers-Veraart network model where the operating cash flows are unrestricted in sign. We propose a mixed-integer programming problem that can be used to compute clearing vectors in this model. Due to the binary variables in this problem, the corresponding (set-valued) systemic risk measure fails to have convex values in general. We associate nonconvex vector optimization problems with the systemic risk measure and provide theoretical results related to the weighted-sum and Pascoletti-Serafini scalarizations of this problem. Finally, we test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters.
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