Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options

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.

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Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion

Statistics & Probability Letters ◽

10.1016/j.spl.2018.11.015 ◽

2019 ◽

Vol 146 ◽

pp. 147-155 ◽

Cited By ~ 11

Author(s):

Yang Yang ◽

Wen Su ◽

Zhimin Zhang

Keyword(s):

Series Expansion ◽

Deficit At Ruin ◽

Fourier Cosine ◽

Cosine Series ◽

Fourier Cosine Series ◽

The Deficit At Ruin

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APPROXIMATING THE DENSITY OF THE TIME TO RUIN VIA FOURIER-COSINE SERIES EXPANSION

Astin Bulletin ◽

10.1017/asb.2016.27 ◽

2016 ◽

Vol 47 (1) ◽

pp. 169-198 ◽

Cited By ~ 7

Author(s):

Zhimin Zhang

Keyword(s):

Risk Model ◽

Series Expansions ◽

Two Dimensional ◽

Numerical Examples ◽

One Dimensional ◽

Fourier Cosine ◽

Cosine Series ◽

Compound Poisson Risk Model ◽

Fourier Cosine Series ◽

Approximation Errors

AbstractIn this paper, the density of the time to ruin is studied in the context of the classical compound Poisson risk model. Both one-dimensional and two-dimensional Fourier-cosine series expansions are used to approximate the density of the time to ruin, and the approximation errors are also obtained. Some numerical examples are also presented to show that the proposed method is very efficient.

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Some Finite Two-Dimensional Contractions

Aeronautical Quarterly ◽

10.1017/s0001925900004480 ◽

1968 ◽

Vol 19 (1) ◽

pp. 91-104

Author(s):

R. D. Mills

Keyword(s):

Velocity Potential ◽

Axisymmetric Flow ◽

Elliptic Functions ◽

Two Dimensional ◽

Fourier Cosine ◽

Cosine Series ◽

Fourier Cosine Series ◽

Form Representation ◽

Axial Velocity Distribution ◽

Similar Series

SummaryGeneral solutions for two-dimensional incompressible potential flow occurring between two equipotential planes perpendicular to the x-axis are given. The first form is the two-dimensional analogue of Thwaites’s solution for axisymmetric flow and allows the calculation of the flow when the axial velocity distribution is specified as a Fourier cosine series in x. The second form of solution, obtained by “inverting” the first form, allows the calculation of the flow when the shape of the “boundary streamline” is specified by a similar series in the velocity potential ϕ.It is shown how the second form of solution may be utilised to design contracting channels between equipotential planes. The computation of the contraction shapes and velocities is straightforward. In particular, contractions are derived from smoothing conditions similar to those used by Thwaites, and from a flow having a single (ϕ, y) step-discontinuity. It is shown in the Appendix that the latter flow possesses a closed form representation in terms of elliptic functions.

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Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Mathematics ◽

10.3390/math7090835 ◽

2019 ◽

Vol 7 (9) ◽

pp. 835 ◽

Cited By ~ 27

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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