Before revision:  This space is denoted by 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 . This space was studied in detail by Cheng and Xu (2013) and we will defined several well-known risk measures on it .
After revision:  This space is denoted by 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 .