Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model

Yuan Gao, Lingju Chen, Jiancheng Jiang and Honglong You
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Yuan Gao: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Lingju Chen: College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China
Jiancheng Jiang: Department of Mathematics and Statistics, School of Data Science, University of North Carolina, Charlotte, NC 28223, USA
Honglong You: School of Statistics, Qufu Normal University, Qufu 273165, China

JRFM, 2020, vol. 13, issue 12, 1-12

Abstract: In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

Keywords: classical risk model; nonparametric estimation; ruin probability (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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