Quite recently, a great interest has been devoted to time-consistency of risk measures in its different formulations (see Delbaen, Follmer and Penner, Bion-Nadal, Delbaen et al., Laeven and Stadje, among many others). However, almost all the papers address to coherent or convex risk measures...

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...