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In this paper, we consider a bidimensional renewal risk model with constantforce of interest, in which the claim size vector with certain localsubexponential marginal distribution and its inter-arrival time are subject toa new time-dependence structure. We obtain the uniform local asymptotics of thetotal net loss process in the model. Moreover, some specific examples of thejoint distribution satisfying the conditions of the dependence structure aregiven. Finally, in order to illustrate a condition of the above result, a localsubexponential distribution is find for the first time that, its localdistribution is not almost decreased.

The uniform local asymptotics of the total net loss process in a new time-dependent bidimensional renewal model