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