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Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks

Author

Listed:
  • Xing-Fang Huang

    (Institute of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China)

  • Ting Zhang

    (Department of Statistics, Nanjing Audit University, Nanjing 211815, China)

  • Yang Yang

    (Institute of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China)

  • Tao Jiang

    (School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China)

Abstract

This paper considered a dependent discrete-time risk model, in which the insurance risks are represented by a sequence of independent and identically distributed real-valued random variables with a common Gamma-like tailed distribution; the financial risks are denoted by another sequence of independent and identically distributed positive random variables with a finite upper endpoint, but a general dependence structure exists between each pair of the insurance risks and the financial risks. Following the works of Yang and Yuen in 2016, we derive some asymptotic relations for the finite-time and infinite-time ruin probabilities. As a complement, we demonstrate our obtained result through a Crude Monte Carlo (CMC) simulation with asymptotics.

Suggested Citation

  • Xing-Fang Huang & Ting Zhang & Yang Yang & Tao Jiang, 2017. "Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks," Risks, MDPI, vol. 5(1), pages 1-14, March.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:1:p:14-:d:92089
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    References listed on IDEAS

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    7. Hashorva, Enkelejd & Li, Jinzhu, 2013. "ECOMOR and LCR reinsurance with gamma-like claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 206-215.
    8. Chen, Yiqing & Liu, Jiajun & Liu, Fei, 2015. "Ruin with insurance and financial risks following the least risky FGM dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 98-106.
    9. Yang, Yang & Ignatavičiūtė, Eglė & Šiaulys, Jonas, 2015. "Conditional tail expectation of randomly weighted sums with heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 20-28.
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    Citations

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    Cited by:

    1. Edita Kizinevič & Jonas Šiaulys, 2018. "The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model," Risks, MDPI, vol. 6(1), pages 1-17, March.
    2. Leipus, Remigijus & Paukštys, Saulius & Šiaulys, Jonas, 2021. "Tails of higher-order moments of sums with heavy-tailed increments and application to the Haezendonck–Goovaerts risk measure," Statistics & Probability Letters, Elsevier, vol. 170(C).
    3. Andrius Grigutis & Jonas Šiaulys, 2020. "Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model," Mathematics, MDPI, vol. 8(2), pages 1-30, January.
    4. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).

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