Before revision:  In this paper, we study the dual representation of quasiconvex risk measures defined on a special space of financial positions, which is called the variable exponent Bochner-Lebesgue space and was studied in detail by Cheng and Xu (2013).
After revision: Since the quasiconvex risk measures is a bigger class than the well known convex risk measures, the study of quasiconvex risk measures makes sense especially in the financial markets with volatility. In this paper, we study the dual representation of quasiconvex risk measures defined on a special space of financial positions, which is called the variable exponent Bochner-Lebesgue space and was studied in detail by Cheng and Xu (2013).