基于复傅里叶级数展开的最低身故利益保障寿险产品的定价  

Valuing Guaranteed Minimum Dea th Benefi ts by Complex Fourier Series Expansion

作　　者：张博 张志民[1] ZHANG Bo;ZHANG Zhimin(College of Mathematics and Statistics,Chongqing University,Chongqing,401331,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《应用概率统计》2022年第1期123-137,共15页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11871121)资助.

摘　　要：本文利用复傅里叶级数展开方法(CFS)对最低身故利益保障(GMDB)寿险产品进行定价,其主要的思想是对辅助函数进行傅里叶级数展开.本文考虑了两种剩余寿命密度函数的形式,即联合指数形式和分段常数死亡率形式,并通过运用已知的Levy模型的特征函数来估计级数的系数.我们将主要考虑看涨期权和看跌期权下GMDB产品的定价问题,在数值实验部分我们还通过与余弦级数展开方法(COS)和蒙特卡洛方法(MC)进行比较来说明CFS在计算精度和运行时间方面的优势.In this paper, we use the complex fourier series expansion method(CFS) to price guaranteed minimum death benefits(GMDB). The main idea is to expand the Fourier series of the auxiliary function.The density function of remaining lifetime has two forms in this paper, namely combination-of-exponentials density and piecewise constant forces of mortality assumption, and the coefficients of series are estimated by using the known characteristic function of the general Lévy model. We mainly consider the value of GMDB products under call options and put options. In the numerical experiment section, we also demonstrate the advantages of CFS in calculation accuracy and running time by comparing with cosine series expansion method(COS) and Monte Carlo method(MC).

关 键 词：CFS方法 最低身故利益保障 看涨期权 看跌期权 Levy模型 

分 类 号：O211.9[理学—概率论与数理统计]