Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Yunyun Wang, Wenguang Yu, Yujuan Huang, Xinliang Yu and Hongli Fan
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Yunyun Wang: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Wenguang Yu: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Yujuan Huang: School of Science, Shandong Jiaotong University, Jinan 250357, China
Xinliang Yu: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Hongli Fan: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China

Mathematics, 2019, vol. 7, issue 3, 1-25

Abstract: In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are exponentially distributed. A new method for estimating the expected discounted penalty function by Fourier-cosine series expansion is proposed. We show that the estimation is easily computed, and it has a fast convergence rate. Some numerical examples are also provided to show the good properties of the estimation when the sample size is finite.

Keywords: compound poisson insurance risk model; expected discounted penalty function; estimation; Fourier transform; Fourier-cosine series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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