最佳的救助策略来自于漂移控制超冷的斯蒂芬问题
Christa Cuchiero1, Christoph Reisinger2, Stefan Rigger3
1Department of Statistics and Operations Research, Data Science @ Uni Vienna, Vienna University, Kolingasse 14-16, A-1090 Vienna, Austria.
概括
中央银行可以通过战略注入现金来限制银行业违约. 最佳的策略包括在特定,时间变化的股权价值范围内补贴银行,以管理系统性风险.
科学领域:
- 金融数学 金融数学
- 量化金融 量化金融
- 风险管理 风险管理
背景情况:
- 银行业的系统性风险对金融稳定构成重大威胁.
- 中央银行是为陷入困境的金融机构提供贷款的最后手段.
- 建模一个中央银行的最佳干预策略是复杂的,因为相互义务和潜在的违约.
研究的目的:
- 确定中央银行需要的最低现金注入量,以将违约限制在预定义的比例.
- 分析中央代理人的控制问题的行为,因为机构的数量变得无限大.
- 为金融机构推出最佳的救助策略,以减轻系统性风险.
主要方法:
- 具有相互义务的结构性违约模型.
- 关于中央代理人的控制问题的一致性分析.
- 平均场控制问题的制定和使用政策梯度方法的数值解决.
- 一个漂移控制超冷的Stefan问题的识别.
主要成果:
- 随着机构数量接近无限,中央代理人的控制问题的值趋同.
- 问题的解决方案被证明是满足一个漂移控制的超冷的斯蒂芬问题.
- 最佳策略是以反形式计算的.
- 模拟显示,在特定的时间依赖区域为股权价值提供补贴的银行是最优的.
结论:
- 中央银行的干预可以有效地管理银行业的系统性风险.
- 最佳的救助策略是动态的,取决于金融机构的股权价值.
- 数学建模提供了对金融稳定最佳政策设计的见解.
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