Summary: Based on previous works by A. Bonanno and M. Reuter [Phys. Rev. D 62, No. 4, 043008 (2000), doi:10.1103/PhysRevD.62.043008; Phys. Rev. D 73, No. 8, 083005 (2006); doi:10.1103/PhysRevD.73.083005], we postulate a renormalization group-improved solution for the exterior of a collapsing object that emits radiation. We show that, contrary to Vaidya’s radiating solution, backscattered radiation is bounded in the eikonal approximation, so that this solution provides us with a more consistent description of the last stages of collapse. We also show its limitations as the exterior of collapsing stars endowed with very high negative pressures. Finally, we are able to describe the profile of the luminosity of a collapsing object as seen by a far away observer in situations where Vaidya’s solution cannot deliver an admissible answer. We illustrate this with models for the collapse of scalar fields where such a profile had not been possible to obtain so far.