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,
maxw(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?
minw( 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.
maxw(w' \mu)
s.t.
w' \Sigma w = \sigma20
w' i = 1
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- GiuseppeAlesii
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analytical solutions / closed forms for classical mean var. portfolio sel.
Last edited by GiuseppeAlesii on August 18th, 2017, 7:32 am, edited 1 time in total.
Re: analytical solutions / closed forms for classical mean var. portfolio sel.
What a coincidence!
Re: analytical solutions / closed forms for classical mean var. portfolio sel.
you both have it for homework?What a coincidence!
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- GiuseppeAlesii
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Re: analytical solutions / closed forms for classical mean var. portfolio sel.
happenstance with which event?What a coincidence!
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- kermittfrog
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Re: analytical solutions / closed forms for classical mean var. portfolio sel.
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.
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.
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- GiuseppeAlesii
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Re: analytical solutions / closed forms for classical mean var. portfolio sel.
thanks, very good hint. I really appreciate.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.