  In this paper we investigate the applicability of a recently introduced
primal-dual splitting method in the context of solving portfolio optimization
problems which assume the minimization of risk measures associated to different
convex utility functions. We show that, due to the splitting characteristic of
the used primal-dual method, the main effort in implementing it constitutes in
the calculation of the proximal points of the utility functions, which assume
explicit expressions in a number of cases. When quantifying risk via the
meanwhile classical Conditional Value-at-Risk, an alternative approach relying
on the use of its dual representation is presented as well. The theoretical
results are finally illustrated via some numerical experiments on real and
synthetic data sets.
