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Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims

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  • Zhu, Lingjiong

Abstract

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give three examples of non-stationary and non-renewal point processes: Hawkes process, Cox process with shot noise intensity and self-correcting point process. We also show some aggregate claims results for these three examples.

Suggested Citation

  • Zhu, Lingjiong, 2013. "Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 544-550.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:544-550
    DOI: 10.1016/j.insmatheco.2013.08.008
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    References listed on IDEAS

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    1. Veraverbeke, N., 1977. "Asymptotic behaviour of Wiener-Hopf factors of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 27-37, February.
    2. Schlegel, Sabine, 1998. "Ruin probabilities in perturbed risk models," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 93-104, May.
    3. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
    4. ., 1998. "Models," Chapters,in: The Handbook of Economic Methodology, chapter 74 Edward Elgar Publishing.
    5. Xiaogu, Zheng, 1991. "Ergodic theorems for stress release processes," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 239-258, April.
    6. Isham, Valerie & Westcott, Mark, 1979. "A self-correcting point process," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 335-347, May.
    7. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
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    Citations

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    Cited by:

    1. repec:eee:stapro:v:127:y:2017:i:c:p:165-172 is not listed on IDEAS
    2. Lingjiong Zhu, 2015. "A State-Dependent Dual Risk Model," Papers 1510.03920, arXiv.org.
    3. Zailei Cheng & Youngsoo Seol, 2018. "Gaussian Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims," Papers 1801.07595, arXiv.org, revised Aug 2019.
    4. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 55-65.
    5. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," LSE Research Online Documents on Economics 64051, London School of Economics and Political Science, LSE Library.
    6. Dassios, Angelos & Zhao, Hongbiao, 2017. "A generalised contagion process with an application to credit risk," LSE Research Online Documents on Economics 68558, London School of Economics and Political Science, LSE Library.
    7. repec:wsi:ijfexx:v:05:y:2018:i:02:n:s2424786318500160 is not listed on IDEAS
    8. Behzad Mehrdad & Lingjiong Zhu, 2014. "On the Hawkes Process with Different Exciting Functions," Papers 1403.0994, arXiv.org, revised Sep 2017.
    9. Seol, Youngsoo, 2015. "Limit theorems for discrete Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 223-229.
    10. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.
    11. Roueff, François & von Sachs, Rainer & Sansonnet, Laure, 2016. "Locally stationary Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1710-1743.

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