大型复杂金融产品投资组合的风险管理与资本监管一直是学者、金融机构和监管部门关注的研究热点。本项目选择近年来交易量的迅猛增长的一类典型复杂金融投资产品——变年金，作为主要研究对象，从单个合约的定价入手，研究大型变年金投资组合的估值、风险对冲和监管资本的理论模型和计算方法。首先，我们将基于柳树法研究在随机利率下适用于多种随机收益模型的多条款变年金合约的定价方法；然后在该方法的基础上利用自动微分和机器学习技术快速有效的计算变年金投资组合的估值与对冲策略，有效的控制整个组合的投资风险；最后，通过分析市场数据与市场风险因素，估计未来市场收益的概率分布，并通过柳树法在选取的典型市场情景下，对组合进行估值，从而替代嵌套模拟方法计算最低监管资本。最终本项目将形成一套适用范围广、计算速度快和稳定性高的大型复杂金融产品投资组合定价和风险管理的理论模型和数值方法。

Risk management and regulatory capital calculation of a large complex portfolio is drawn a lot of attention from researchers, practitioners and regulators. We focus our research on the typical complex financial product, variable annuity (VA), whose trading volume is increased rapidly recently. The goal of this project is to build up theoretic models and numerical methods for pricing, hedging and risk managing a large VA portfolio. To achieve the goal, we first propose a pricing scheme for a single VA contract, whose underlying reference fund follows some popular stochastic processes, embedded with different guaranteed riders under a willow tree framework. Then, the automatic differentiation and machine learning techniques are employed to valuate and hedge a large VA portfolio. Finally, we analyze the multi-factor models and market data of the reference fund future market returns to obtain an approximate distribution for the future returns. Based on the approximate distribution, some typical market scenarios are generated so that the minimal required regulatory capital for the VA portfolio can be evaluated through the proposed willow tree method without running nested simulations. As a result of this project, we will propose a universal, efficient and stable theoretical model and numerical method for the large complex portfolio valuation and risk management.