Let $X$ be a normal distribution with mean $\mu$ and variance $\sigma^2$. Furthermore we have a constant $\rho$. Suppose our probability space is carrying a filtration. Now I want to calculate the following conditional expectation:
$E[e^X\mathcal1_{\{X>f(\rho)\}}\mid\mathcal{F}_t]$
where $f$ is a deterministic function. Similar I want also to calculate
$E[\mathcal1_{\{X>f(\rho)\}}\mid\mathcal{F}_t]$
How can I calculate this? Thanks for you help
hulik