If I have a two correlated normal distributed random variables, i.e. $A \sim N(m_a,\sigma_a^2)$ and $B \sim N(0,1)$, with correlation coefficient $ Corr(A,B) =\rho$, then I want to define a random variable $ R = e^{\frac{1}{2}A}B$.
I found out that $ E[R] = \frac{1}{2} \rho \sigma_a^2 e^{\frac{1}{2}m_a + \frac{1}{8}\sigma_a^2}$
My question: What ist $E[R^2]$ ?