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

Yang, Yang; Su, Wen; Zhang, Zhimin

doi:10.1016/j.spl.2018.11.015

Cited by 26 publications

(18 citation statements)

References 18 publications

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“…Since then, it has become a standard tool for studying ruin related quantities. We refer the interested readers to Lin et al [40], Huang and Yu [41], Ruan et al [42], Li et al [43], Wang et al [44], Yang et al [45], Yu [46,47], Yuen et al [48], Huang et al [49], Xie and Zou [50].…”

Section: Introductionmentioning

confidence: 99%

On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Guo

Wang

et al. 2020

Mathematics

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In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

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Section: Introductionmentioning

confidence: 99%

On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Guo

Wang

et al. 2020

Mathematics

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“…Except for option pricing, this method has been adopted in insurance ruin theory. For example, Chau et al [25,26] used the 1D COS method to compute the ruin probability and the expected discounted penalty function; Zhang [27] approximated the density function of the time to ruin by both 1D and 2D COS methods; Yang et al [28] proposed a nonparametric estimator for the deficit at ruin by the 2D COS method; Wang et al [29] and Huang et al [30] used the 1D COS method to estimate the expected discounted penalty function under some risk models with stochastic premium income. The COS method has also been used by some authors to value variable annuities.…”

Section: Introductionmentioning

confidence: 99%

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Yong

Guan

et al. 2019

Mathematics

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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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“…As a special type of Gerber-Shiu functions, the ruin probability is estimated by Mnatsakanov et al [31], Masiello [32], and Zhang et al [33] under the classical compound Poisson risk model. Further, Zhang [34] and Yang et al [35] estimated the finite ruin probability by double Fourier transform. For the general Gerber-Shiu function, Shimizu [36] estimated it by Laplace inversion in the compound Poisson insurance risk model.…”

Section: Introductionmentioning

confidence: 99%

Estimating the Gerber-Shiu Expected Discounted Penalty Function for Lévy Risk Model

Huang

Pan

et al. 2019

Discrete Dynamics in Nature and Society

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This paper studies the statistical estimation of the Gerber-Shiu discounted penalty functions in a general spectrally negative Lévy risk model. Suppose that the claims process and the surplus process can be observed at a sequence of discrete time points. Using the observed data, the Gerber-Shiu functions are estimated by the Laguerre series expansion method. Consistent properties are studied under the large sample setting, and simulation results are also presented when the sample size is finite.

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

Cited by 26 publications

References 18 publications

On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Estimating the Gerber-Shiu Expected Discounted Penalty Function for Lévy Risk Model

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