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 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 BRITE-Constellation photometry of π5 Orionis, an ellipsoidal SPB variable

2020 ◽  
Vol 496 (2) ◽  
pp. 2391-2401 ◽  
Author(s):  
M Jerzykiewicz ◽  
A Pigulski ◽  
G Handler ◽  
A F J Moffat ◽  
A Popowicz ◽  
...  
Keyword(s):  
Primary Component ◽  
Evolutionary Stage ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fundamental Parameters ◽  
Fourier Cosine Series ◽  
Orbital Frequency ◽  
Low Amplitude ◽  
Hipparcos Parallax ◽  
Better Than

ABSTRACT Results of an analysis of the BRITE-Constellation photometry of the SB1 system and ellipsoidal variable π5 Ori (B2 III) are presented. In addition to the orbital light-variation, which can be represented as a five-term Fourier cosine series with the frequencies forb, 2forb, 3forb, 4forb, and 6forb, where forb is the system’s orbital frequency, the star shows five low-amplitude but highly significant sinusoidal variations with frequencies fi (i = 2, .., 5, 7) in the range from 0.16 to 0.92 d−1. With an accuracy better than 1σ, the latter frequencies obey the following relations: f2 − f4 = 2forb, f7 − f3 = 2forb, f5 = f3 − f4 = f7 − f2. We interpret the first two relations as evidence that two high-order ℓ = 1, m = 0 gravity modes are self-excited in the system’s tidally distorted primary component. The star is thus an ellipsoidal SPB variable. The last relations arise from the existence of the first-order differential combination term between the two modes. Fundamental parameters, derived from photometric data in the literature and the Hipparcos parallax, indicate that the primary component is close to the terminal stages of its main-sequence (MS) evolution. Extensive Wilson–Devinney modelling leads to the conclusion that best fits of the theoretical to observed light curves are obtained for the effective temperature and mass consistent with the primary’s position in the HR diagram and suggests that the secondary is in an early MS evolutionary stage.

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 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.

Sign in / Sign up

Export Citation Format

Share Document