SAAM Algorithm

SAAM Algorithm

All  algorithms used in this app can use the Lagrange Multiplier Method to solve given problems. And all of these can be reduced to the following format:

\(max\{E(\omega^T r_{n+1}）-\lambda Var(\omega^T r_{n+1})\} \qquad (*)\)

Let \(W=\omega^T r_{n+1}\) and using the knowledge of probability theory, it is easy to know

\(Var(W)=E(Var(W|R_n))+Var(E(W|R_n)) \)

So, when the expected return and covariance matrix are assumed to be known, just as the assumption in Markowitz algorithm, the second part is zero, which is against with the ground truth.

In this way, SAAM algorithm is proposed, using Bayes theory.