Effective potential in finite formulation of QFT

In recent works [1,2], we have shown how n-point correlation functions in perturbative QFT can be computed without running into intermediate divergences. Here we want to illustrate explicitly that one can calculate the quantum effective potential by the same method. As a main example, we consider a theory with two fields having large and small vacuum expectation values (vev). We show that no fine-tuning between the physical quantities is needed to keep the hierarchy between the vevs of different fields.