bearish wrote:GiuseppeAlesii wrote:hi there,

I am looking for

-- a numerical method

and

-- a closed form solution

for the expected return formulation of the classical mean variance portfolio optimization problem.

max_{w}(w' \mu)

s.t.

w' \Sigma w = \sigma^{2}_{0}

w' i = 1

Could someone please let me know some references about this?

The Wikipedia entry on modern portfolio theory is not bad

Thanks a lot for your post, but it does not suit to my query which is much more specific.

In particular, I have a doubt that the usual Lagrangian constrained optimization framework applies to the case of return maximization formulation. To be specific, in the first order condition related to the constraint on volatility weights appear squared and with cross products. And this prevents the derivation of a system of linear equations like in the dual problem, i.e. risk minimization given an expected portfolio return.