本项目拟考虑保单持有人的行为风险，基于随机分析、随机控制、统计计算和数值模拟等理论，探讨养老年金产品的定价及相关问题。考虑不同养老年金的特点，选取适当的定价模型，采用风险中性定价理论和无差别定价理论，重点考虑保单持有人的退保行为和保单账户价值提取行为，通过多种数值方法，对传统养老年金和新型养老年金分别进行定价。同时，将新型养老年金引入到生命周期模型中，考虑保单持有人的收入风险、死亡风险和健康风险，探讨保单持有人的最优消费-投资问题和退休福利问题。本项目所涉及的研究内容均是国际保险精算界研究的热点问题，一方面将驱动无差别定价理论和生命周期模型的理论研究，另一方面，将推动我国养老年金市场的进一步发展，为完善我国的养老保险体系提供有力的理论支撑。

Applying theories of stochastic analysis, stochastic control, statistical calculation and numerical simulation, we will study valuation and relevant problems of annuities with policyholders’ behaviour risk. We divide annuities into two categories, traditional annuities and new annuities. Focusing on surrender options and withdrawal options, we will consider valuations of different annuities using different numerical methods. We will adopt risk-neutral theories and indifference-pricing theories. Furthermore, we will consider how to select optimal consumption-investment strategies by adopting new annuities into life-cycle models. In the model, we will consider policyholders’ income risk, mortality risk and health risk. This project will promote research on indifference pricing and life-cycle models. Meanwhile, this project will provide valuable suggestions to the development of annuities in China.