英文标题：
《Gaussian Process Regression for Pricing Variable Annuities with
  Stochastic Volatility and Interest Rate》
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作者：
Ludovic Gouden\\`ege and Andrea Molent and Antonino Zanette
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最新提交年份：
2019
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英文摘要：
  In this paper we investigate price and Greeks computation of a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity (VA) when both stochastic volatility and stochastic interest rate are considered together in the Heston Hull-White model. We consider a numerical method the solves the dynamic control problem due to the computing of the optimal withdrawal. Moreover, in order to speed up the computation, we employ Gaussian Process Regression (GPR). Starting from observed prices previously computed for some known combinations of model parameters, it is possible to approximate the whole price function on a defined domain. The regression algorithm consists of algorithm training and evaluation. The first step is the most time demanding, but it needs to be performed only once, while the latter is very fast and it requires to be performed only when predicting the target function. The developed method, as well as for the calculation of prices and Greeks, can also be employed to compute the no-arbitrage fee, which is a common practice in the Variable Annuities sector. Numerical experiments show that the accuracy of the values estimated by GPR is high with very low computational cost. Finally, we stress out that the analysis is carried out for a GMWB annuity but it could be generalized to other insurance products.
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中文摘要：
在本文中，我们研究了在赫斯顿-赫尔-怀特模型中同时考虑随机波动率和随机利率时，保证最小提取收益（GMWB）可变年金（VA）的价格和计算。我们考虑一种数值方法来解决动态控制问题，这是由于计算了最优取款。此外，为了加快计算速度，我们采用了高斯过程回归（GPR）。从之前为一些已知模型参数组合计算的观测价格开始，可以在定义的域上近似整个价格函数。回归算法包括算法训练和评估。第一步最耗时，但只需执行一次，而后一步速度非常快，只需在预测目标函数时执行。所开发的方法，以及用于计算价格和希腊货币的方法，也可用于计算无套利费用，这是可变年金行业的常见做法。数值实验表明，探地雷达估计值精度高，计算量小。最后，我们强调，该分析是针对GMWB年金进行的，但也可以推广到其他保险产品。
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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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