Nonparametric estimation of ruin probability by a new method in the perturbed compound Poisson model. (Chinese. English summary) Zbl 07809946

Zhang, Bo; Liu, Chaolin; Yu, Wenguang; Li, Jing

Chin. J. Appl. Probab. Stat. 39, No. 5, 643-658 (2023).

Summary: In this paper, we consider the nonparametric estimation of the ruin probability in a compound Poisson risk model perturbed by diffusion. We approximate the ruin probability based on the complex Fourier series expansion (CFS) method, and use a random sample on claim number and individual claim sizes to construct a nonparametric estimator of the ruin probability. We also perform an error analysis of the estimator under a large sample size, and provide simulation results to verify the effectiveness of this estimation method under a finite sample size.

MSC:

62P05

Applications of statistics to actuarial sciences and financial mathematics

Keywords:

ruin probability; perturbed compound Poisson model; nonparametric estimator; CFS method

References:

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