In this presentation, we consider inference problem about the drift parameter in generalized exponential Ornstein-Uhlenbeck processes with unknown change-point in the context of unknown number of base functions. In particular, we consider the case where the drift parameter may satisfy some restrictions. We propose estimators for the number of base functions and the change-point. We also derive the unrestricted estimator, the restricted estimator and shrinkage estimators as well as their asymptotic properties. Finally, to illustrate the performance of the proposed method, we present some simulation results and analyze some real financial datasets. Beyond these interesting contributions, the novelty of this approach consists in the fact that we overcome the difficulties dues to the randomness fact of the dimensions of the derived estimators.