  Loop quantum gravity is believed to eliminate singularities such as the big
bang and big crunch singularity. This belief is based on studies of so-called
loop quantum cosmology which concerns symmetry-reduced models of quantum
gravity. In this paper, the problem of singularities is analysed in the context
of the Bohmian formulation of loop quantum cosmology. In this formulation there
is an actual metric in addition to the wave function, which evolves
stochastically (rather than deterministically as the case of the particle
evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs
whenever this actual metric is singular. It is shown that in the loop quantum
cosmology for a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker
space-time with arbitrary constant spatial curvature and cosmological constant,
coupled to a massless homogeneous scalar field, a big bang or big crunch
singularity is never obtained. This should be contrasted with the fact that in
the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
