Suppose $X_t$ and $Y_t$ both have standard normal distributions with mean zero and variance 1. What is the $E_t[e^{aX_t + bY_t^2}]$ where $a$ and $b$ are constants?
It should be something like:
$E_t[e^{aX_t + bY_t^2}]=e^{0.5a^2 + 2*b^2 + ab \times cov(X_t, Y_t^2)}$
Am I right? If so, how to compute the last covariance knowing $Cov_t(X_t, Y_t) = c$, where $c% is a constant.