Estimating the Gerber–Shiu function by Fourier–Sinc series expansion

Zhimin Zhang

29 citations0/0 files storedScandinavian Actuarial Journal

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Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

Abstract

In this paper, we consider the nonparametric estimation of the Gerber–Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient estimator based on Fourier–Sinc series expansion. Our estimator is easily computed and has a faster convergence rate. Some simulation examples are provided to show that the estimator performs well when the sample size is finite.

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References

1998On the Time Value of Ruin 1998On the discounted penalty at ruin in a jump-diffusion and the perpetual put option 1970An extension of the renewal equation and its application in the collective theory of risk 2002A generalized defective renewal equation for the surplus process perturbed by diffusion 2009The perturbed compound Poisson risk model with two-sided jumps 2005The Gerber–Shiu function in a Sparre Andersen risk process perturbed by diffusion 2001On the discounted distribution functions of the surplus process perturbed by diffusion 2008Nonparametric estimation of ruin probabilities given a random sample of claims

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