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3

The formula is $$\mu = \lambda CX$$ in your notation. You find it in many places, e.g. here. The assumption is that you know $\lambda$ which is a strong assumption. Furthermore it only holds if investors are unconstrained (long/short not long only). It is intuitive as it says that given the weighting the return expectation increases with risk aversion ...

0

It is difficult to say what is not working with your code. Try Matlab's quadratic programming function quadprog() instead. This function specializes in solving this optimization problem. The syntax is: $$x = quadprog(H,f,A,b,Aeq,beq,lb,ub)$$

0

Portfolios for some kind of investors effectively balance asset investments with liabilities incurred. Think about a pension account, where the future liability of the pension payment represents the liability and the currently invested monies are the assets. I am sure you can think of other similar situations but I will illustrate regarding pensions below. ...

2

Try fmincon for solving (1)-(4).

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if you have $p=0.5$ For example: $U(w)=ln(2w)$ why is that? relative risk aversion is given by $$RRA=\frac{-wU''(w)}{U('w)}=\frac{-w*(-1/4w^2)}{1/2w}=0.5$$ Now you can apply your formula. take for example: $x= 10000$ and $\pi=0.5=1-\pi.$ then expected utility is equal to $EU(x,w)=0.5*ln(2*(w+x))+0.5*ln(2*(w-x))=0.5ln(220000)+0.5ln(180000)$ you want to ...

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