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could anyone tell me a reference where I can find the analytical solution of the risk aversion formulation of the classical mean variance portfolio optimization problem,
max_w(w' \mu - \lambda w' \Sigma w)
s.t.
w' i = 1
 akin to the closed forms which can be derived through constrained optimization using Lagrange multipliers for the risk minimization formulation?
min_w( w' \Sigma w )
s.t.
w' \mu = \mu₀
w' i = 1
Also, could anyone tell me the reference for a closed form solution of the expected return formulation of the same classical mean variance portfolio optimization problem.
max_w(w' \mu) 

s.t.
w' \Sigma w = \sigma²₀
w' i = 1

What a coincidence!

What a coincidence!

you both have it for homework?

What a coincidence!

happenstance with which event?

If i remember correctly, the first set optimization equations are derived using exponential utility.

So the expected utility formula should be something like E(exp(-a*x)).

Yet, I assume that you are rather interested in the closed form solution to this equation - this would make itself available by googling along the lines of "linear algebra portfolio selection". Then, select result 1.

If i remember correctly, the first set optimization equations are derived using exponential utility.

So the expected utility formula should be something like E(exp(-a*x)).

Yet, I assume that you are rather interested in the closed form solution to this equation - this would make itself available by googling along the lines of "linear algebra portfolio selection". Then, select result 1.

thanks, very good hint. I really appreciate.