英文标题：
《A unified pricing of variable annuity guarantees under the optimal
  stochastic control framework》
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作者：
Pavel V. Shevchenko and Xiaolin Luo
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最新提交年份：
2016
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英文摘要：
  In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the existing numerical methods. For numerical valuation of these contracts, we develop a direct integration method based on Gauss-Hermite quadrature with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is very efficient when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We also present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a benchmark for practitioners and researchers developing pricing of variable annuity guarantees.
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中文摘要：
在本文中，我们回顾了许多国家向散户投资者提供的可变年金生前和死后担保的定价。投资者购买这些产品是为了利用市场增长和保护储蓄。我们通过最优随机控制框架给出了这些产品的定价，并回顾了现有的数值方法。对于这些合同的数值估值，我们开发了一种基于高斯-埃尔米特求积的直接积分方法，使用一维三次样条计算预期合同价值，并使用双三次样条插值在合同现金流事件时间内应用跳跃条件。与偏微分方程方法相比，如果在事件时间之间以闭合形式已知合同下风险资产的转移密度（或其矩），则该方法非常有效。我们还提供了市场上可用的最低累积保障（GMAB）担保定价的准确数值结果，可作为制定可变年金担保定价的从业者和研究人员的基准。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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