  The measurements of the muon and electron anomalous magnetic moments hint at
physics beyond the standard model. We show why and how models inspired by
asymptotic safety can explain deviations from standard model predictions
naturally. Our setup features an enlarged scalar sector and Yukawa couplings
between leptons and new vector-like fermions. Using the complete two-loop
running of couplings, we observe a well-behaved high energy limit of models
including a stabilization of the Higgs. We find that a manifest breaking of
lepton universality beyond standard model Yukawas is not necessary to explain
the muon and electron anomalies. We further predict the tau anomalous magnetic
moment, and new particles in the TeV energy range whose signatures at colliders
are indicated. With small CP phases, the electron EDM can be as large as the
present bound.
