英文标题：
《Valuation of Variable Annuities with Guaranteed Minimum Withdrawal and
  Death Benefits via Stochastic Control Optimization》
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作者：
Xiaolin Luo and Pavel V. Shevchenko
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最新提交年份：
2015
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英文摘要：
  In this paper we present a numerical valuation of variable annuities with combined Guaranteed Minimum Withdrawal Benefit (GMWB) and Guaranteed Minimum Death Benefit (GMDB) under optimal policyholder behaviour solved as an optimal stochastic control problem. This product simultaneously deals with financial risk, mortality risk and human behaviour. We assume that market is complete in financial risk and mortality risk is completely diversified by selling enough policies and thus the annuity price can be expressed as appropriate expectation. The computing engine employed to solve the optimal stochastic control problem is based on a robust and efficient Gauss-Hermite quadrature method with cubic spline. We present results for three different types of death benefit and show that, under the optimal policyholder behaviour, adding the premium for the death benefit on top of the GMWB can be problematic for contracts with long maturities if the continuous fee structure is kept, which is ordinarily assumed for a GMWB contract. In fact for some long maturities it can be shown that the fee cannot be charged as any proportion of the account value -- there is no solution to match the initial premium with the fair annuity price. On the other hand, the extra fee due to adding the death benefit can be charged upfront or in periodic instalment of fixed amount, and it is cheaper than buying a separate life insurance.
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中文摘要：
在本文中，我们提出了一个在最优投保人行为下，结合保证最低提取福利（GMWB）和保证最低死亡福利（GMDB）的可变年金的数值估值，并将其作为一个最优随机控制问题来解决。该产品同时处理财务风险、死亡风险和人类行为。我们假设金融风险的市场是完全的，通过卖出足够的保单，死亡风险是完全多样化的，因此年金价格可以表示为适当的预期。用于求解最优随机控制问题的计算引擎基于一种鲁棒有效的三次样条高斯-厄米特求积方法。我们给出了三种不同类型的身故保险金的结果，并表明，在最佳投保人行为下，如果保持连续的费用结构，在GMWB合同中通常假设的连续费用结构，则在GMWB的基础上增加身故保险金可能会有问题。事实上，对于一些长期到期的债券，可以证明不能按账户价值的任何比例收取费用——没有办法将初始保费与公平年金价格相匹配。另一方面，由于增加死亡抚恤金而产生的额外费用可以预先收取，也可以定期分期支付，而且比购买单独的人寿保险更便宜。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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