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optimization proble risk parity

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I state that I am not very experienced in MATLAB. I should create and minimize a function to find the weights of an asset allocation problem. The problem is as follow:
Minimize ∑(RC(Fj)/σP−1/M)^2 for j=1:M
sub ∑x=1
where RC(Fj) = (A⊤x)j⋅ (A+Σx/√x⊤Σx)j
where
  • A is a loadings matrix
  • A+ is Moore-Penrose inverse of A
  • Σ is a covariance matrix
  • x is a weights vector
I would need some codes to solve these problems. Thank you in advance.

Accepted Answer

Rishik Ramena
Rishik Ramena on 31 Dec 2020
MATLAB does have a toolbox dedicated to solving optimization problems like these. Do have a look at its documentation for the ramp up.
  1 Comment
Tommaso Delicato
Tommaso Delicato on 16 Jan 2021
I cannot extract the j-th component of the vector which is calculated as the product of the part (A+Σx/√x⊤Σx)j.
Can you tell me how?

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