maximisation of the utility function , portfolio optimization
14 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
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 Kommentare
Torsten
am 7 Feb. 2023
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.
Akzeptierte Antwort
Torsten
am 7 Feb. 2023
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 Kommentare
Torsten
am 8 Feb. 2023
Bearbeitet: Torsten
am 8 Feb. 2023
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)
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Multiobjective Optimization finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!