Hello everybody,

does anyone have an idea how to prove the following inequality

$\displaystyle E(\log(1+c_1(e^{Z+b}-1)))\geq E(\log(1+c_2(e^{Z+b}-1)))$?

where $\displaystyle Z$ is normally distributed with a non-negative mean and $\displaystyle c_1,c_2$ are constants with $\displaystyle c_1,c_2 \in [0,1],c_1\geq c_2$

$\displaystyle b>0$ is also a constant.

Thanks in advance