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The Perturbed Compound Poisson Risk Process with Investment and Debit Interest

Author

Listed:
  • Chuancun Yin

    (Qufu Normal University)

  • Chunwei Wang

    (Qufu Normal University)

Abstract

In this paper, we study absolute ruin questions for the perturbed compound Poisson risk process with investment and debit interests by the expected discounted penalty function at absolute ruin, which provides a unified means of studying the joint distribution of the absolute ruin time, the surplus immediately prior to absolute ruin time and the deficit at absolute ruin time. We first consider the stochastic Dirichlet problem and from which we derive a system of integro-differential equations and the boundary conditions satisfied by the function. Second, we derive the integral equations and a defective renewal equation under some special cases, then based on the defective renewal equation we give two asymptotic results for the expected discounted penalty function when the initial surplus tends to infinity for the light-tailed claims and heavy-tailed claims, respectively. Finally, we investigate some explicit solutions and numerical results when claim sizes are exponentially distributed.

Suggested Citation

  • Chuancun Yin & Chunwei Wang, 2010. "The Perturbed Compound Poisson Risk Process with Investment and Debit Interest," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 391-413, September.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9109-z
    DOI: 10.1007/s11009-008-9109-z
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    References listed on IDEAS

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    Cited by:

    1. Jun Cai & Hailiang Yang, 2014. "On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest," Annals of Operations Research, Springer, vol. 212(1), pages 61-77, January.
    2. Ramsden, Lewis & Papaioannou, Apostolos D., 2019. "Ruin probabilities under capital constraints," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 273-282.
    3. Hao Ma & Jian Pan & Lei Lv & Guanghui Xu & Feng Ding & Ahmed Alsaedi & Tasawar Hayat, 2019. "Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    4. Yin, Chuancun & Wen, Yuzhen, 2013. "An extension of Paulsen–Gjessing’s risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 469-476.
    5. Liu, Bing & Meng, Hui & Zhou, Ming, 2021. "Optimal investment and reinsurance policies for an insurer with ambiguity aversion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    6. 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.
    7. Junxia Ma & Qiuling Fei & Fan Guo & Weili Xiong, 2019. "Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems," Mathematics, MDPI, vol. 7(12), pages 1-16, November.
    8. Wen Su & Wenguang Yu, 2020. "Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model," Mathematics, MDPI, vol. 8(10), pages 1-11, September.
    9. Lijuan Wan & Ximei Liu & Feng Ding & Chunping Chen, 2019. "Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    10. Feng Ding & Jian Pan & Ahmed Alsaedi & Tasawar Hayat, 2019. "Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    11. Chuancun Yin & Yuzhen Wen, 2013. "An extension of Paulsen-Gjessing's risk model with stochastic return on investments," Papers 1302.6757, arXiv.org.

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