Utility maximization optimal weights

Hello,

I face this problem in matlab:

Im trying to maximize a utility function for an investor ........i use power utility function U(w)=(((1-W)^1-gamma))-1)/(1-gamma) for the beggining

W: wealth W=(1+rp)

and rp = portfolio expected return rp=(w1*r1+w2*r2+.....+wn*rn) ------>(r1,r2....rn ) : is the matrix returns in excel file with 10 assets and 60 montlhy observation

and gamma: is risk averse with constant values

So everything is known except from weights (w1,w2,w3....wn) I need to find optimal weights which maximize expected utility with a constraint sum(w)=1

This is a optimzation problem but in dont know how to solve it ! i think one way is fmincon to minimize the negative expected utility but i dont know how to use it.

[Emanuele De Angelis]

create your obj funcion. Use fmincon with starting points (eg. zeros for weights) and all necessary bound.

Remember: put a minus in the objective function (you want maximize it)