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In this paper, we consider a by-claim risk model with a constant rate of interest force, in which the main claims and the by-claims form a sequence of pTQAI nonnegative random variables and all their distributions belong to the dominatedly-varying heavy-tailed subclass. We obtain the asymptotically upper and lower bound formulas of the ultimate ruin probability for such a by-claim risk model. As its by-products, some interesting properties for pTQAI structure are also investigated. The results extend some existing ones in the literature. [ABSTRACT FROM AUTHOR]

Consider a non standard continuous-time renewal risk model with a constant force of interest, in which the claim sizes are assumed to be conditionally linearly wide dependent (CLWD) and belong to the intersection of dominatedly varying tailed and long tailed class, and inter-arrival times are assumed to be a sequence of independent and identically distributed random variables independent of the claim sizes. Under some technical conditions, we obtain an asymptotic formula for the tail probability of discounted aggregate claims, which holds locally uniform for all time horizon within a finite interval. When the claim sizes are further restricted to be consistently varying tailed, we show that this asymptotic formula is globally uniform for all time horizon within an infinite interval. [ABSTRACT FROM AUTHOR]

In this article we obtain some novel results on pairwise quasi-asymptotically independent (pQAI) random variables. Concretely speaking, letX1, …,Xnbenreal-valued pQAI random variables, andW1, …,Wnbe anothernnon negative and arbitrarily dependent random variables, but independent ofX1, …,Xn. Under some mild conditions, we prove thatW1X1, …,WnXnare still pQAI as well. Our result is in a general setting whether the primary random variablesX1, …,Xnare heavy-tailed or not. Finally, a special case of above result is applied to risk theory for investigating the finite-time ruin probability for a discrete-time risk model with a wide type of dependence structure. [ABSTRACT FROM AUTHOR]