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Mathematics 2019, 7(3), 305; https://doi.org/10.3390/math7030305

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

1
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
2
School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
3
School of Science, Shandong Jiaotong University, Jinan 250357, China
*
Author to whom correspondence should be addressed.
Received: 24 February 2019 / Revised: 15 March 2019 / Accepted: 18 March 2019 / Published: 26 March 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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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. View Full-Text
Keywords: compound poisson insurance risk model; expected discounted penalty function; estimation; Fourier transform; Fourier-cosine series compound poisson insurance risk model; expected discounted penalty function; estimation; Fourier transform; Fourier-cosine series
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Wang, Y.; Yu, W.; Huang, Y.; Yu, X.; Fan, H. Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income. Mathematics 2019, 7, 305.

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