非线性期望理论与基于模型不确定性的风险度量

Non-linear Expectation Theory and Risk Measurement Based on Model Ambiguity

本文首先利用自回归条件异方差过程的多变点识别方法揭示经济、金融数据的内在演变规律,以阐明现行/经典的概率统计理论和方法在经济、金融领域的不完全适用性及相应领域概率统计模型不确定性存在的根源、必然性及其具体表现形式。进而,通过诠释非线性期望理论对概率统计模型均值不确定性、方差不确定性、分布形状不确定性的理论构建、模型设计与量化分析方式及其基于无穷概率分布审慎测算风险的原理,论证了随机分析与计算领域的这一国际领先成就将成为引致风险管理等领域深刻变革的重要技术理论与工具。最后,文章实证展示了基于模型不确定性的风险度量的审慎性与有效性,以期切实助益于涵纳不确定性的审慎风险管理这一我国及世界经济、金融界亟待攻克的重大理论与现实问题。

With the approach of multiple-change-point detection for auto-regressive conditional heteroskedastic processes, the paper first demonstrates that economic and financial data have uncertain characteristics of probability and statistics, and thus illustrates the limited applicability of current probability theory in a realistic, dynamic economic environment. Then, we analyze how non-linear expectation theory incorporates all kinds of uncertainty, such as volatility uncertainty and mean uncertainty, in risk modelling and measures risk with infinite amount of possible uncertain distributions. Meanwhile the analysis shows that this recent progress in stochastic analysis and calculus might bring fundamental change to risk management theory and practice. And empirical evidence of the effectiveness of risk measurement based on model ambiguity is provided. Thus, the paper is to contribute to the cutting edge research on uncertainty analysis and risk management and to provide important technical support for managing and maintaining financial stability.