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

Qiuying Zhang and Fengyang Cheng

Scandinavian Actuarial Journal, 2018, vol. 2018, issue 5, 450-463

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 $.

Date: 2018
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DOI: 10.1080/03461238.2017.1377106

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