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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]

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]