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Asymptotics for the ruin probability of a time-dependent renewal risk model with geometric Lévy process investment returns and dominatedly-varying-tailed claims

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  • Fu, Ke-Ang
  • Ng, Cheuk Yin Andrew

Abstract

Consider a continuous-time renewal risk model, in which the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. Suppose that the surplus is invested in a portfolio whose return follows a Lévy process. When the claim-size distribution is dominatedly-varying tailed, asymptotic estimates for the finite- and infinite-horizon ruin probabilities are obtained.

Suggested Citation

  • Fu, Ke-Ang & Ng, Cheuk Yin Andrew, 2014. "Asymptotics for the ruin probability of a time-dependent renewal risk model with geometric Lévy process investment returns and dominatedly-varying-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 80-87.
  • Handle: RePEc:eee:insuma:v:56:y:2014:i:c:p:80-87
    DOI: 10.1016/j.insmatheco.2014.04.001
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    References listed on IDEAS

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    1. Tang, Qihe & Wang, Guojing & Yuen, Kam C., 2010. "Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 362-370, April.
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    5. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.
    6. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    7. 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.
    8. Chen, Yiqing & Ng, Kai W., 2007. "The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 415-423, May.
    9. Susanne Emmer & Claudia Klüppelberg, 2004. "Optimal portfolios when stock prices follow an exponential Lévy process," Finance and Stochastics, Springer, vol. 8(1), pages 17-44, January.
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