On the Fourier cosine series expansion method for stochastic control problems

2013 ◽  
Vol 20 (4) ◽  
pp. 598-625 ◽  
Author(s):  
M.J. Ruijter ◽  
C.W. Oosterlee ◽  
R.F.T. Aalbers
Keyword(s):  
Stochastic Control ◽  
Series Expansion ◽  
Expansion Method ◽  
Control Problems ◽  
Stochastic Control Problems ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Series Expansion Method

scholarly journals Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1402
Author(s):  
Wen Su ◽  
Yunyun Wang
Keyword(s):  
Series Expansion ◽  
Risk Model ◽  
Insurance Risk ◽  
Transform Method ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Surplus Process ◽  
Fourier Cosine Series ◽  
The Fourier Transform ◽  
Better Than

In this paper, we propose an estimator for the Gerber–Shiu function in a pure-jump Lévy risk model when the surplus process is observed at a high frequency. The estimator is constructed based on the Fourier–Cosine series expansion and its consistency property is thoroughly studied. Simulation examples reveal that our estimator performs better than the Fourier transform method estimator when the sample size is finite.

scholarly journals Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 835 ◽  
Author(s):  
Wenguang Yu ◽  
Yaodi Yong ◽  
Guofeng Guan ◽  
Yujuan Huang ◽  
Wen Su ◽  
...  
Keyword(s):  
Density Function ◽  
Series Expansion ◽  
Numerical Experiments ◽  
Random Variable ◽  
Actuarial Science ◽  
Exponential Distributions ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Exponential Lévy Process

Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method.

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