受国内通货膨胀及长寿风险影响，及受如美国金融危机等复杂国际环境影响，风险控制成为我国养老基金投资管理面临的大问题。传统风险度量和建模方法越来越不适应复杂多变的市场环境。非参数建模方法不需事先设定要估计的模型具有特定形式，模型构建由样本数据驱动，具有很强的适应性。本项目基于VaR、CVaR和Basel II/III 等先进下方风险度量，利用非参数建模方法构建相关随机因素的随机过程模型、给出下方风险的计算公式，根据各种实际需要，在不同市场设置下，利用均值-下方风险和下方风险约束下效用最大化准则构建DB 型、DC 型、DB 与DC 混合型养老基金投资决策模型。利用随机控制、数值迭代和智能优化等方法对模型进行分析性求解或数值求解，借助计量方法和计算机技术对所得结果进行实证分析与模拟检验，作出经济解释。其研究成果将丰富并发展养老基金投资管理理论，为我国养老基金管理部门投资决策和风险监控提供科学建议。

Influenced by the domestic inflation and longevity risks, as well as by the current complex international economic situations, such as the American Financial Crisis, financial risk has become a more and more important problem confronted by pension fund managers. However, traditional risk measures and modeling methods become more and more unadapted to the complicated and changing market environments. It is well known that the nonparametric modeling methods do not impose any particular form on the models, and the modeling results are completely driven by sample data. Therefore, the nonparametric modeling method has wide adaptability and practicability. In this project, we will derive the formulas for the current mainstream downside risk measures (such as Value at Risk, Conditional Value-at-Risk and Basel II/III) and construct the stochastic process models for relevant random factors by using the nonparametric modeling method. We then will establish dynamic multi-period or continuous-time mean-downside risk model and expected utility maximization model with downside risk control by considering together with the influence of relevant stochastic factors, legal restrictions and actual requirements. Based on these models, we next study the investment management problems for the following types of pension funds: defined benefit (DB), defined contribution (DC) and hybrid of DB and DC under different market hypotheses. By utilizing approaches such as stochastic optimal control, stochastic analysis, numerical iteration, intelligent optimization and so on, we will also seek analytical or numerical solutions for these models. We will further explore empirical analysis by econometric approach on the research results and computer simulations by advanced Monte Carlo and quasi-Monte Carlo methods. Finally, we will give economic explanation about our research results. Therefore, the research results of this project will not only enrich the theory of pension fund investment management, but also provide useful scientific advice to the pension fund managers and supervision departments in our country to make their investment strategies and to control the risks on investments. Hence, this project has both important practical significance and potential applications.