Risk measures with markets volatility

Fei Sun, Yijun Hu

Published 2018-06-04Version 1

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.