A Goal Programming Model with Satisfaction Function for Risk Management   and Optimal Portfolio Diversification
  We extend the classical risk minimization model with scalar risk measures to the general case of set-valued risk measures. The problem we obtain is a set-valued optimization model and we propose a goal programming-based approach with satisfaction function to obtain a solution which represents the best compromise between goals and the achievement levels. Numerical examples are provided to illustrate how the method works in practical situations. 
Davide La Torre and Marco Maggis
q-fin.RM math.PR