Portfolio Optimization with Quasiconvex Risk Measures

Abstract

In this paper, we focus on the portfolio optimization problem associated to a quasiconvex risk measure (satisfying some additional assumptions). For coherent/convex risk measures, the portfolio optimization problem has been already studied by Gaivoronski and Pflug (2005), Rockafellar and Uryasev (2000) and Ruszczynski and Shapiro (2006), among others. Following the approach of Ruszczynski and Shapiro (2006) but by means of quasiconvex analysis and notions of subdifferentiability, we characterize optimal solutions of the portfolio problem associated to quasiconvex risk measures. The shape of the efficient frontier in the mean-risk space and some particular cases are also investigated.

Keywords: quasiconvex risk measures, portfolio optimization, convex risk measures, efficient frontier

JEL Classification: C61, G11