Convex risk minimization via proximal splitting methods

Understand

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.