Miccolis Variance formula
I'm getting stuck on the support for the risk load. Bahnemann/the wiki write
Var(S)=E(N)Var(X;L)+Var(N)[E(X;L)^2]
Isn't S = X*N? If so, isn't Var(S) = Var(XN) = E(X^2)*E(N^2) - [E(X)^2]*[E(N)^2] = [E(N)^2]*Var(X)+Var(N)*E(X^2) ?
I'm not able to get to Bahnemann's equation.
Comments
Your expression for Var(S) is incorrect, it violates the law of total variance. The correct formula is the compound variance formula https://en.wikipedia.org/wiki/Compound_probability_distribution
which is what Bahnemann states in the wiki.