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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.
Acknowledgements
The author would like to thank the editor and two referees for their valuable suggestions which significantly improved the paper.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This research was supported by the National Natural Science Foundation of China [grant number 11471058], [grant number 11661074]; the Natural Science Foundation Project of CQ CSTC of China [grant number cstc2014jcyjA00007]; and MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant number 16YJC910005].