maximisation of the utility function , portfolio optimization
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Hi,
I am trying to miximize a utility function of an investor , I use CRRA utility
,
,
,
is known such that
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1286950/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287300/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287305/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287310/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287315/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287320/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287325/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287330/image.png)
So , everthing is known except from the weights ( x_1,...,x_4) , I need to find the optimal weights $x_i$ which maximize expected utility with constraint
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1286965/image.png)
I don't know how to solve this optimization problem , does this problem nonlinear optimization problem ?
Thank you
2 个评论
Torsten
2023-2-7
R_t is a time-dependent random variable ? What distribution follow its components ?
sum_{i=1}^{i=4} x_i*R_t is meant to be x(1)*R_t(1,:) + x(2)*R_t(2,:) + x(3)*R_t(3,:) + x(4)*R_t(4,:) ?
How is u(c) defined with c being a vector ?
I guess E[...] is expectation ?
You need to explain your problem in more detail to get an answer.
采纳的回答
Torsten
2023-2-7
Calculate W1*Rt1, W2*Rt2,...,W4*Rt4. Let Wi*Rti be maximum. Then (assuming gamma < 1) x_i = 1, x_j = 0 for i~=j is optimal.
8 个评论
Torsten
2023-2-8
编辑:Torsten
2023-2-8
is there any different function I can apply it to compare the results ?
You could try "ga".
For completeness, you should add the bound constraints
lb = zeros(4,1);
ub = ones(4,1);
as lower and upper bound constraints for the x(i):
W = ...;
R = ...;
gamma = ...;
Aeq = [1 1 1 1];
beq = 1;
lb = zeros(4,1);
ub = ones(4,1);
u = @(x) 1/(1-gamma)*x.^(1-gamma);
obj = @(x)-sum(u(x.'*W*R));
x = fmincon(obj,0.25*ones(1,4),[],[],Aeq,beq,lb,ub)
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