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

2016 ◽  
Vol 47 (1) ◽  
pp. 169-198 ◽  
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.

scholarly journals Estimating the Gerber-Shiu Function in a Compound Poisson Risk Model with Stochastic Premium Income

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Yunyun Wang ◽  
Wenguang Yu ◽  
Yujuan Huang
Keyword(s):  
Convergence Rate ◽  
Risk Model ◽  
Compound Poisson ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Compound Poisson Risk Model ◽  
Fourier Cosine Series ◽  
Fast Convergence Rate ◽  
Premium Income ◽  
Poisson Risk Model

In this paper, we consider the compound Poisson risk model with stochastic premium income. We propose a new estimation of Gerber-Shiu function by an efficient method: Fourier-cosine series expansion. We show that the estimator is easily computed and has a fast convergence rate. Some simulation examples are illustrated to show that the estimation has a good performance when the sample size is finite.

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 Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Zhihua Zhang
Keyword(s):  
Asymptotic Formula ◽  
Stochastic Processes ◽  
Hyperbolic Cross ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Approximation Errors ◽  
Asymptotic Representations

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions.

Some Finite Two-Dimensional Contractions

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.

scholarly journals A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Fuzhen Pang ◽  
Haichao Li ◽  
Yuan Du ◽  
Shuo Li ◽  
Hailong Chen ◽  
...  
Keyword(s):  
Series Solution ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Cross Sectional ◽  
Numerical Examples ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Fourier Series Method ◽  
Edge Conditions

A series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibration displacements and the cross-sectional rotations of the midplane are represented by a double Fourier cosine series and four supplementary functions. The supplementary functions are expressed as the combination of trigonometric functions and a single cosine series expansion and are introduced to remove the potential discontinuities associated with the original admissible functions along the edges when they are viewed as periodic functions defined over the entire x-y plane. This series solution is approximately accurate in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. The convergence, accuracy, stability, and efficiency of the proposed method have been examined through a series of numerical examples. Some numerical examples about the nondimensional frequency and mode shapes of Mindlin rectangular plates with different point-supported edge conditions are given.

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