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Interplay of financial and insurance risks in dependent discrete-time risk models

Author

Listed:
  • Yang, Yang
  • Jiang, Tao
  • Wang, Kaiyong
  • Yuen, Kam C.

Abstract

Consider a discrete-time insurance risk model with two kinds of risks, i.e., insurance and financial risks. Within period i, the real-valued net insurance loss caused by traditional claims is regarded as the insurance risk, denoted by Xi, and the positive stochastic discount factor over the same time period is the financial risk, denoted by Yi. Assume that {(X,Y),(Xi,Yi),i≥1} form a sequence of independent and identically distributed random vectors. This work investigates the interplay of the insurance and financial risks, allowing a dependence structure exists between these two kinds of risks. Following the work of Li and Tang (2015), we derive some asymptotic and uniformly asymptotic formulas for the finite-time and infinite-time ruin probabilities, under the assumption that the generic random vector (X,Y) follows a bivariate Sarmanov distribution and every convex combination of the distributions of X and Y is of strongly regular variation. As an extension, we further consider a general pair (X,Y), whose dependence structure is more verifiable than the Sarmanov one to some extent. In such a setting, we study the asymptotic tail behavior of the product XY, which forms an analogue of the well-known Breiman’s theorem in a different and dependent situation.

Suggested Citation

  • Yang, Yang & Jiang, Tao & Wang, Kaiyong & Yuen, Kam C., 2020. "Interplay of financial and insurance risks in dependent discrete-time risk models," Statistics & Probability Letters, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:stapro:v:162:y:2020:i:c:s0167715220300559
    DOI: 10.1016/j.spl.2020.108752
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    References listed on IDEAS

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    1. Xin-mei Shen & Zheng-yan Lin & Yi Zhang, 2009. "Uniform Estimate for Maximum of Randomly Weighted Sums with Applications to Ruin Theory," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 669-685, December.
    2. Norberg, Ragnar, 1999. "Ruin problems with assets and liabilities of diffusion type," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 255-269, June.
    3. Zhang, Yi & Shen, Xinmei & Weng, Chengguo, 2009. "Approximation of the tail probability of randomly weighted sums and applications," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 655-675, February.
    4. Yang, Yang & Su, Wen & Zhang, Zhimin, 2019. "Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 147-155.
    5. Nyrhinen, Harri, 1999. "On the ruin probabilities in a general economic environment," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 319-330, October.
    6. Nyrhinen, Harri, 2001. "Finite and infinite time ruin probabilities in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 265-285, April.
    7. Asimit, Alexandru V. & Jones, Bruce L., 2008. "Dependence and the asymptotic behavior of large claims reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 407-411, December.
    8. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
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    Cited by:

    1. Wang, Bingjie & Li, Jinzhu, 2024. "Asymptotic results on tail moment for light-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 43-55.

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