 In this paper, we will study some risk measures with markets volatility. These risk measures are defined on a special space of financial positions, which is called the variable exponent Bochner-Lebesgue space. 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 . The dual representations for them are also provided.
Since the risk in financial markets has become much more uncertain and volatile than before, the usual risk measures may be limited when dealing with the risk management. In this paper, we will study several classes of risk measures on a special space 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 representations for them are also provided.
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Since the risk in financial markets has become much more uncertain and volatile than before, the usual risk measures may be limited when dealing with the risk management.
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some risk measures with markets volatility. These risk measures are defined
several classes of risk measures
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of financial positions, which is called the variable exponent Bochner-Lebesgue space. This space is denoted by
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. This space was studied in detail by Cheng and Xu (2013) and we will defined several well-known risk measures on it