Vacuum stability of supersymmetric extended Higgs sectors with a discrete symmetry

We study vacuum stability of supersymmetric extended Higgs sectors with a discrete $Z_2$ symmetry. These models may be able to explain dark matter, neutrino masses, baryon asymmetry of the Universe and hierarchy problem simultaneously at the TeV scale. This $Z_2$ symmetry could be broken spontaneously. We examine the stability of the $Z_2$ symmetric vacuum at the tree level in several models with such extended Higgs sectors.