how to minimize distance with optimization
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hi all i am new member i did had some difficulties to express my point, here is the real problem: i did optimize moments at the variance unit=0.0003 so i did get Z1* Z2* Z3*
now the problem is how to optimize the portfolio so that mean,skewness kurtosis are near the optimum value Z1* Z2* Z3* at the same time under investor preferences parameters ex alpha=1 beta=0 gamma=0 so the investor is more interested in mean return. i have to solve
minimize Z=(0.0003+d1)^alpha +(0.0003+d3)^beta +(0.0003+d4)^gamma
subject to
mean(Rtilt*X) +d1=Z1* (mean +d1=Z1*)
mean(((Rtilt*X)-mean(Rtilt*X)).^3)/(.0003*sqrt(.0003)) +d3=Z3* (skewness +d3=Z3*)
mean(((Rtilt*X)-mean(Rtilt*X)).^4)/(.0003*.0003) +d4=Z4* (kurtosis +d4=Z4*)
somme Xi=1 and 0=<Xi=<0.35 d1,d3,d4 >=0
X'*V*X=0.0003 V(7x7)=cov(Rtilt)
alpha,beta,gamma are known numbers (investor preferences)
Z1*,Z3*,Z4* are known numbers (goals)
Rtilt is known matrix (132x7) : returns
i want to minimize distances(unknown) d1,d3,d4 to get my vector of weights X(7x1):unknown.
alpha,beta,gamma are parameteres that i use it can be(1,0,0) or anything i want.
what function to use ? i tried fgoalattain but am not sure cause i cant handle parameters alpha beta gamma.
Thanks
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回答(1 个)
Torsten
2016-4-1
The problem as stated does not have a solution since it is unbounded.
Choose
x1=(M-9)/4, x2=(M+3)/4 and y=(13-M)/4
for arbitrary M.
Then you get M as the value of your objective function, and your constraints are satisfied.
Best wishes
Torsten.
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