Portfolio optimization with quasiconvex risk measures

In this paper, we focus on the portfolio optimization problem associated with a quasiconvex risk measure (satisfying some additional assumptions). For coherent/convex risk measures, the portfolio optimization problem has been already studied in the literature. Following the approach of Ruszczyński and Shapiro [Ruszczyński A, Shapiro A (2006) Optimization of convex risk functions. Math. Oper. Res. 31(3):433-452.], but by means of quasiconvex analysis and notions of subdifferentiability, we characterize optimal solutions of the portfolio problem associated with quasiconvex risk measures. The shape of the efficient frontier in the mean-risk space and some particular cases are also investigated.