Optimization Problem about Optimal Portfolio with Aversion Index

Question

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Hello everyone, I'm trying to due with following optimization problem:

I have done some of the coding but cannot finish the double summation part.

Does anyone have any ideas that could help??? Thanks in advance.

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Answer 1

Alan Weiss 2019-2-4

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I don't see your rho and sigma variables, but you could try

sumexpr = optimexpr;
for i = 1:n
    for j = 1:n
        sumexpr = sumexpr + w(i)*w(j)*rho(i,j)*sigma(i)*sigma(j);
    end
end

It would undoubtedly be more efficient to write this double summation as a standard MATLAB matrix multiplication, something like

sumexpr = w'*M*w;

where M has an appripriate definition, but the double sum should work, too.

Alan Weiss

MATLAB mathematical toolbox documentation

KA HEI LAM 2019-2-4

Thanks for the reply. I tried the following double summation:

w'*ann_std'*corrlation*ann_std*w

but there is an error:

Error using optim.internal.problemdef.MatrixOperator

Inner matrix dimensions must agree.

Error in optim.internal.problemdef.Mtimes

Error in *

I have calculated the rho and sigma with n-by-n and 1-by-n matrix respectively. Is there any problem?

Alan Weiss 2019-2-4

I suggest that you use the debugger to find out what sizes the variables have just before the times operation executes.

Alan Weiss

MATLAB mathematical toolbox documentation