基于非线性数学期望的系统性风险测度与防控方法研究

With the joint effort of researchers in risk management，（macro）finance， and mathematics, the project will apply the distinguished achievements of Prof. Peng, an academician of Chinese Academy of Science, in stochastic analysis and calculus to developing new models and tools for measuring and managing systemic risk. The global financial turmoils in recent years have highlighted the necessity and importance of managing systemic risk at a national/international level and attracted researchers and policy makers across countries to devote to the daunting task. The purpose of this project is to contribute to the cutting edge research on systemic risk and, at the same time, contribute to the estabishiment of China's counter-cyclical, macro-prudential financial management system which is emphasized in China's 12th Five-Year plan. Specifically，we will develop nonlinear risk measurement models in contrast to the linear models which have been advocated by Prof. Robert Merton at Harvard University, a Nobel Prize winner, since 2002 and especially after the 2007-2008 Subprime Crisis. We will also study the complex mechanism of risk contagion in macrofinance to come up with systemic risk forewarning indicators. The new models and related numerical analysis will not only based on rigorous theoretical deduction but also be tested through a mass of simulations facilitated by powerful computer hardward and softwares. Moreover, the project will leverage the invaluable resources of the 2011 collaborative innovation center for "Quantitative Analysis and Calculation in Financial Risk Management" to conduct both theoretical and empirical research. As the project proceeds, we will routinely introduce our research findings to the international academia through seminars, SSCI papers, and international conferences. And as another main expected achievement of the project, the nonlinear risk measurement models and systemic risk forewarning indicators are about to be a significant technical support for managing and maintaining China's macrofinancial stability.

本项目通过金融风险理论、金融数学与（宏观）金融三领域的联合研究，针对我国及世界经济、金融界亟待解决的现实问题，基于随机分析与随机计算领域的国际领先成果，探索非线性数学期望理论框架下的系统性风险测度方法；研究系统性风险的复杂演变机制与速度；编制相应的预警指标体系并测算指标阈值。非线性风险测度模型及其相关算法的厘定、验证及优化将不仅建立在理论论证与计算机模拟测试的基础上，同时将利用国家2011金融风险定量计算与控制协同创新中心提供的协同平台进行实证研究。项目预期成果将以国际期刊论文的形式向国际相关学术领域介绍更为精益的系统性风险度量模型和相关成果；而项目生成的系统性风险度量与防控方法将助益于我国建立系统性风险监控机制。

.本项目的立题背景是：在国际层面，近年来世界经济领域在金融风险管理与控制方面出现了较大问题且实体经济在金融动荡中不断受到恶性冲击；在国内，随着我国面临的国际、国内经济金融形势日益复杂，国家一再强调“守住不发生系统性金融风险的底线”。因而，本研究的目的是致力于探讨世界经济、金融平稳发展中务需攻克的问题；研究内容属于当前国际相关学术界致力于探索和实现理论突破的前沿问题以及国际相关政策界亟待实现监管实践创新的领域。...本项目的主要研究内容是通过金融与数学等相关学科的跨学科交叉研究、联合攻关，提出更为审慎、更为符合我国金融市场发展现状且兼顾国际前沿理论突破的系统性风险管理技术。...研究所取得的重要结果及其科学意义概述如下：率先突破非线性期望理论这一发源于我国的随机分析与计算国际领先成果的应用实现，攻克了其应用落地中最显著的国际难题——均值与波动率上下限的确定问题，并进一步通过算法创新开拓了非线性期望理论的数值实现。首度分层次、分因子论证了该理论应用于风险测度的特有优势。进而，在非线性期望理论框架下，创新了一类基础性概率统计不确定性模型——随机极限正态分布，可更为精准的刻画金融数据的现实分布形态，从而为解决长久困扰金融监管界与实业界的厚尾风险建模测度问题提供了有效的理论与实证支持。创新了非线性期望理论框架下的G-CCA方法，从而将CCA方法进益至对经济学发展具有重要意义的“不确定性”假设条件下更为敏锐、审慎的风险计量与分析模型，且尤其更为适合我国金融市场发展的现状与经济、金融数据的现状；同时通过纳入漂移率风险因素，将动态预期资产收益率对金融风险的重要影响纳入了风险分析范畴，进一步实质性优化与完善了CCA这一重要宏、微观金融风险监管模型。...如上相关研究进展将不仅是对相应数学领域的有益贡献，且将切实助益于我国具有自主知识产权的风险管理技术的储备与创新，促进系统性风险审慎监管理论、方法和实践的国际前沿理论攻关与技术提升。

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