  As systemic risk has become a hot topic in the financial markets, how to
measure, allocate and regulate the systemic risk are becoming especially
important. However, the financial markets are becoming more and more
complicate, which makes the usual study of systemic risk to be restricted. In
this paper, we will study the systemic 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. Finally, the dual representation
for this new systemic risk measures will be studied. Our results show that
every this new systemic risk measure can be decomposed into a convex certain
function and a simple-systemic risk measure, which provides a new ideas for
dealing with the systemic risk.
