HETEROGENEOUS COMPUTATION OF RAINBOW OPTION PRICES USING FOURIER COSINE SERIES EXPANSION UNDER A MIXED CPU-GPU COMPUTATION FRAMEWORK

2014 ◽  
Vol 21 (2) ◽  
pp. 91-104 ◽  
Author(s):  
A. Cassagnes ◽  
Y. Chen ◽  
H. Ohashi
Keyword(s):  
Series Expansion ◽  
Option Prices ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series

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.

scholarly journals A Mode-Matching Solution for TE-Backscattering from an Arbitrary 2D Rectangular Groove in a PEC

2020 ◽  
Vol 20 (3) ◽  
pp. 159-163 ◽  
Author(s):  
Mehdi Bozorgi
Keyword(s):  
Singular Integrals ◽  
Logarithmic Singularity ◽  
Linear Equations ◽  
Mode Matching ◽  
Electric Conductor ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Highly Oscillatory Integrals ◽  
Rectangular Groove

In this paper, the simple yet effective mode-matching technique is utilized to compute TE-backscattering from a 2D filled rectangular groove in an infinite perfect electric conductor (PEC). The tangential magnetic fields inside and outside of the groove are represented as the sums of infinite series of cosine harmonics (half-range Fourier cosine series). By applying the continuity of the tangential magnetic field, these modes are matched on the groove to obtain the series coefficients by solving a system of linear equations. For this purpose, some oscillatory logarithmic singular integrals involving Hankel and trigonometric functions are solved numerically, starting by removing the logarithmic singularity via integration by parts. In the following, the new well-behaved highly oscillatory integrals are computed using efficient methods, and several comparisons are made to demonstrate the validity and ability of the presented procedure.

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