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We study a discrete-time risk model of double dependence structures. The insurance company can make two investments, namely, risk-free and risky investments. The claim sizes follow a dependence structure, we assume that the dependence structure is one-sided linear process in which innovations is independent and identically distributed (i.i.d.), the innovations and financial risks are also form a dependence structure. When the distributions of the innovations belong to the intersection of the dominated-variation class and the class of long-tailed distributions, we derive some asymptotic formulas for the finite-time ruin probability.

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