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Uniform Estimate for Maximum of Randomly Weighted Sums with Applications to Ruin Theory

Author

Listed:
  • Xin-mei Shen

    (Zhejiang University)

  • Zheng-yan Lin

    (Zhejiang University)

  • Yi Zhang

    (Zhejiang University)

Abstract

This paper obtains the uniform estimate for maximum of sums of upper-tail independent and heavy-tailed random variables with nonnegative dependent random weights. Then the applications to ruin probabilities in a discrete time risk model with dependent gross losses and dependent stochastic returns are considered.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:4:d:10.1007_s11009-008-9090-6
    DOI: 10.1007/s11009-008-9090-6
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    References listed on IDEAS

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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    2. 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.
    3. 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.
    4. 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.
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    Citations

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    Cited by:

    1. 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).
    2. Manuel Ordóñez Cabrera & Andrew Rosalsky & Andrei Volodin, 2012. "Some theorems on conditional mean convergence and conditional almost sure convergence for randomly weighted sums of dependent random variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 369-385, June.
    3. Wang, Yinfeng & Yin, Chuancun, 2010. "Approximation for the ruin probabilities in a discrete time risk model with dependent risks," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1335-1342, September.
    4. Chen Yu & Zhang Weiping & Liu Jie, 2010. "Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(2), pages 1-11, July.
    5. Shijie Wang & Yueli Yang & Yang Liu & Lianqiang Yang, 2023. "Asymptotics for a Bidimensional Renewal Risk Model with Subexponential Main Claims and Delayed Claims," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-13, September.
    6. Zhengyan Lin & Xinmei Shen, 2013. "Approximation of the Tail Probability of Dependent Random Sums Under Consistent Variation and Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 165-186, March.
    7. Liu Yan & Zhang Qinqin, 2015. "Uniform Estimate for Randomly Weighted Sums of Dependent Subexponential Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 9(2), pages 303-318, July.

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