DC型养老金最优资产配置与给付方案问题研究

项目名称： DC型养老金最优资产配置与给付方案问题研究

项目编号： No.71501178

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 管理科学

项目作者： 何林

作者单位： 中国人民大学

项目金额： 17.4万元

中文摘要： DC型养老金为缴费确定，给付不确定，并且与投资收益、给付方案以及生存者利益相关联的一类养老金。如何通过合理的资产配置策略和给付方案设计，为参保人提供最大的养老效用，是养老金管理者和参保人都关注的重要问题。本课题将建立更为符合养老金管理实践的模型。本课题将研究带策略约束的养老金最优资产配置问题；养老金最优转换时间问题；长寿风险下的养老金管理问题，以及带有最小给付要求的养老金最优策略问题。这些模型转化为时间不一致条件下的带约束优化问题，以及市场不完备条件下的约束优化问题。这些问题的提出，需要融合鞅方法和变分方法的精髓，拓展鞅测度变换、鞅分解、HJB变分方法、SDE比较定理等控制优化领域的方法和理论，创造性地加以解决。本课题的研究成果对随机控制优化领域有重要的理论贡献。同时，研究成果为养老金策略制定者提供政策建议，为养老金管理者提供策略参考，为参保人提供业绩基准，为金融监管机构提供监控依据。

中文关键词： DC型养老金；最优资产配置；最优给付；随机最优控制；HJB方程

英文摘要： Defined contribution pension plan is the kind of pension plan that the contribution is predetermined and the benefit outgo is determined by the investment return, benefit outgo and the mortality credit. The management of the pension controls the asset allocation and benefit outgo policies to achieve the maximal old-care utility of the pension members. The models are refined to meet the pension management practices. The following models will be established, the optimal control policies of the pension with constraints on the control policies; optimal conversion time of the pension plan; optimal control problem of the pension under the longevity risk backgrounds; optimal control problem of the pension with minimal benefit outgo constraints, etc. These are the stochastic optimization problems with constrains in the time inconsistent framework, and optimization problems with constrains in the incomplete market framework. In order to solve the complicated stochastic control problems, we need to integrate the martingale method and the variational method innovatively, and extend the Girsanov transformation, martingale decomposition, HJB variational methods and SDE comparison theorem to derive the closed-form solutions. The results have important theoretical contributions to the stochastic optimal control theorems. Meanwhile, the results provide policy suggestions for pension policy makers, provide strategic references for pension managements, provide performance benchmarks for the members, and provide supervision bases for financial regulators.

英文关键词： DC penison plan;optimal asset allocation;optimal benefit outgo;stochastic optimal control;HJB equations