  Using path-integral Quantum Monte Carlo we study the low-temperature phase
diagram of a two-dimensional superconductor within a phenomenological model,
where vortices have a finite mass and move in a dissipative environment modeled
by a Caldeira-Leggett term. The quantum vortex liquid at high magnetic fields
exhibits superfluidity and thus corresponds to a {\em superinsulating} phase
which is characterized by a nonlinear voltage-current law for an infinite
system in the absence of pinning. This superinsulating phase is shifted to
higher magnetic fields in the presence of dissipation.
