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Ruin with insurance and financial risks following the least risky FGM dependence structure

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  • Chen, Yiqing
  • Liu, Jiajun
  • Liu, Fei

Abstract

Recently, Chen (2011) studied the finite-time ruin probability in a discrete-time risk model in which the insurance and financial risks form a sequence of independent and identically distributed random pairs with common bivariate Farlie–Gumbel–Morgenstern (FGM) distribution. The parameter θ of the FGM distribution governs the strength of dependence, with a smaller value of θ corresponding to a less risky situation. For the subexponential case with −1<θ≤1, a general asymptotic formula for the finite-time ruin probability was derived. However, the derivation there is not valid for the least risky case θ=−1. In this paper, we complete the study by extending it to θ=−1. The new formulas for θ=−1 look very different from, but are intrinsically consistent with, the existing one for −1<θ≤1, and they offer a quantitative understanding on how significantly the asymptotic ruin probability decreases when θ switches from its normal range to its negative extremum.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:62:y:2015:i:c:p:98-106
    DOI: 10.1016/j.insmatheco.2015.03.007
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    References listed on IDEAS

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    Cited by:

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    3. Daniel Tawiah Pabifio, 2024. "Sensitivity Analysis of Ruin of an Insurance Company in Ghana," Papers 2410.11846, arXiv.org.
    4. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    5. 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).
    6. Chen, Yiqing, 2017. "Interplay of subexponential and dependent insurance and financial risks," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 78-83.
    7. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    8. Yang Yang & Shuang Liu & Kam Chuen Yuen, 2022. "Second-Order Tail Behavior for Stochastic Discounted Value of Aggregate Net Losses in a Discrete-Time Risk Model," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2600-2621, December.

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