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This article mainly considers the uniform asymptotics for the finite-time ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims. In this model, the two claim-number processes are arbitrarily dependent and each of them is generated by widely orthant dependent claim inter-arrival times. Two types of ruin are studied and for each type of ruin, an asymptotic formula for the finite-time ruin probability is established. These formulae possess a certain uniformity feature in the time horizon. [ABSTRACT FROM AUTHOR]

In this paper, we consider a dependent risk model, in which the claim sizes are ofdependence structure, their inter-arrival times are independent, identically distributed (i.i.d.), and the claim size and its corresponding inter-arrival time satisfy a certain dependence structure described via the conditional distribution of the inter-arrival time given the subsequent claim size being large. We obtain the asymptotics of the lower and upper bounds of precise large deviations for the aggregate amount of claims, which holds uniformly for allxin an infinite interval oft. [ABSTRACT FROM AUTHOR]

This paper investigates tail behavior of the randomly weighted sum ∑nk = 1θkXkand reaches an asymptotic formula, whereXk, 1 ⩽k⩽n, are real-valued linearly wide quadrant-dependent (LWQD) random variables with a common heavy-tailed distribution, and θk, 1 ⩽k⩽n, independent ofXk, 1 ⩽k⩽n, arennon-negative random variables without any dependence assumptions. The LWQD structure includes the linearly negative quadrant-dependent structure, the negatively associated structure, and hence the independence structure. On the other hand, it also includes some positively dependent random variables and some other random variables. The obtained result coincides with the existing ones. [ABSTRACT FROM PUBLISHER]