Can you approximate semi-variance optimization using the MAD model and a piecewise linearization? Hint: See Hamza and Janssen (1995).  Extend the failed model XXXXXXXXXXfor shortfall probability to...

Can you approximate semi-variance optimization using the MAD model

and a piecewise linearization? Hint: See Hamza and Janssen (1995).

 Extend the failed model (5.25) for shortfall probability to lower partial

moments of degrees k = 1, 2,3, 4. What do you observe?