Abstract: This paper establishes a risk model for an insurer with càdlàg investment returns and heavy-tailed claim sizes which are bivariate upper tail independent. On one hand, we propose condition (6), under which a uniform asymptotic estimate of the finite-time ruin probability in the risk model is obtained. On the other hand, considering the universality of condition (6), we find that the condition (6) can be easily verified by some important stochastic processes, such as the Lévy process, Vasicek model, Cox-Ingersoll-Ross (CIR) model, and Heston model.