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:  In this paper, we will study the 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).