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

Author

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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)

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.

Suggested Citation

  • Yunyun Wang & Wenguang Yu & Yujuan Huang & Xinliang Yu & Hongli Fan, 2019. "Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income," Mathematics, MDPI, vol. 7(3), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:305-:d:217201
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    References listed on IDEAS

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