 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). This space is denoted by L^{p(\cdot) (\Omega, E) }  where the variable exponent p(\cdot) is no longer a given real number like the space L^{p}, but a measurable function .
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 will study the quasiconvex risk measures defined on a special space (\Omega, E) } L^{p(\cdot) where the variable exponent p(\cdot) is no longer a given real number like the space L^{p}, but a random variable, which reflects the possible volatility of the financial markets. The dual representation for this quasiconvex risk measures will also provided .
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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.
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study the dual representation of
will study the
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of financial positions, which is called the variable exponent Bochner-Lebesgue space and was studied in detail by Cheng and Xu (2013). This space is denoted by L^{p(\cdot)
A
L^{p(\cdot)
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measurable function
random variable, which reflects the possible volatility of the financial markets. The dual representation for this quasiconvex risk measures will also provided