多元动态风险度量模型及其在投资组合中的应用研究

Based on the problem that static model is lack of dynamic consistency, unable to realize a multi-period dynamic risk measurement, the project is provided the compute method of VaR and CvaR，according to the multi stage characteristics of investment process, researched the theory and method of dynamic risk measurement from the multi-period and continuous time, extended the static model to the multi-dynamic by the volatility model, and constructed a new time coherent risk measurement and risk measurement index by stochastic analysis method. Established the dynamic portfolio selection model and solved the optimal portfolio of using stochastic control theory and the martingale method, and demonstrated research. The model is applied to the risk evaluation and supervision of financial cooperation between China and Arabia. Conquered the measurement difficulties of VaR of multi-abnormal through constructing several new computing method of multi-dynamic VaR model, and preferable solving the peak and fat tail and volatility concentration of financial rate of return. The model can solve the problem of renewing the dynamic information in current time and achieve the multi-period risk measurement that static risk measurement cannot, take the change of financial market information as part of the model parameters, control the market risk in current time according to the change of market, provide the real-time monitoring tool for market supervision, achieve the property requests of dynamic risk measurement frame, provide the scientific basis and references for the risk supervision and investment decision.

针对静态模型缺乏动态持续性，无法实现多时期动态风险度量的问题，本项目根据投资过程的多阶段特点，从多时期及连续时间投资角度研究动态风险度量的理论与方法，通过时变波动模型将静态模型扩展到多元动态情形，用随机分析的方法构造新的时间一致性动态风险测度类和风险度量指标，给出多元动态VaR与CVaR的计算方法，建立动态投资组合选择模型，利用随机控制理论与鞅方法求解投资组合，进行实证研究。将模型应用于中阿金融合作的风险评估与监管。通过构建几种新的计算多元动态VaR模型的方法，较好地解决金融收益率序列的尖峰厚尾性和波动集聚性，克服多元非正态条件下VaR的测算困难。解决静态风险度量理论不能实时更新动态信息无法实现多期风险度量的问题，将金融市场信息的变化作为模型参数的一部分，根据市场变化实时控制市场风险，为市场监管提供实时监控工具，实现动态风险度量框架的属性要求，为风险监管以及进行投资决策提供科学依据和参考。

本项目针对静态模型缺乏动态持续性，无法实现多时期动态风险度量的问题，根据投资过程的多阶段特点，通过时变波动模型将静态VaR和CVaR扩展到动态情形，研究多元动态风险度量的模型与方法。考虑实际投资环境中存在的各种约束要求，提出了一个新的多阶段指数追踪优化模型，计算追踪误差的CVaR风险。考虑动态性或时变特征，探索恰当的满足Bellman 最优性原理条件的动态一致性风险度量方法，用随机分析的方法构造新的时间一致性动态风险测度类，提出了更加简单的多元动态CVaR风险度量的计算方法。研究各种度量极端金融风险的模型和方法，用新型的统计动态结构模型来计算金融市场的VaR 值，探讨金融收益率序列的尖峰厚尾性和波动集聚性的处理方法。建立了基于多元动态SVt-EVT-Vine Copula模型和基于马尔科夫转换的SVt-EVT-Vine Copula模型计算投资组合VaR的方法，实证研究结果表明这些模型对金融风险的预测更加准确合理、有效。研究了保险风险模型的破产概率及最优控制策略问题，获得了最优再保险策略和最小破产概率的显示表达式。用随机分析的方法研究了期权定价问题，推广了Black-Scholes模型的应用。本项目的实施加深了人们对动态风险度量模型与投资组合的认识，为动态风险度量模型与投资组合的深入研究奠定了基础。