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Precise local large deviations for heavy-tailed random sums with applications to risk models

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  • Qiuying Zhang
  • Fengyang Cheng

Abstract

In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common heavy-tailed distribution F, where F(x+Δ)=F((x,x+T])$ F(x+\Delta )=F((x, x+T]) $ is an O$ \mathcal O $-regularly varying function for some fixed constant T>0$ T>0 $(finite or infinite). We also obtain some results on precise local large deviation probabilities for the claim surplus process of generalized risk models in which the premium income until time t is simply assumed to be a nondecreasing and nonnegative stochastic process. In particular, the results we obtained are also valid for the global case, i.e. case T=∞$ T=\infty $.

Suggested Citation

  • Qiuying Zhang & Fengyang Cheng, 2018. "Precise local large deviations for heavy-tailed random sums with applications to risk models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(5), pages 450-463, May.
  • Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:450-463
    DOI: 10.1080/03461238.2017.1377106
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