We report numerical simulations supported by experimental observations of self-focusing, fillamentation, and supercontinuum generation by an optical vortex beam in a Kerr nonlinear medium in the regime of dominating nonlinearity. Despite the strong self-focusing resulting in multiple filaments ordered along the vortex ring the optical vortex remains well preserved at the exit of the nonlinear medium and in the far-field. The presented quasi-(3+1)- dimensional numerical simulations under azimuthal initial vortex ring perturbations confirm qualitatively the experimentally observed survival of the optical vortex in the course of the white light generation.