An interactive approach to stochastic programming-based portfolio optimization

We consider expected return, Conditional Value at Risk, and liquidity criteria in a multi‐period portfolio optimization setting modeled by stochastic programming. We aim to identify a preferred solution of the decision maker (DM) by obtaining information on her/his preferences. We use a weighted Tchebycheff program to generate representative sets of solutions. Our approach models the stochasticity of market movements by stochastic programming. Working with multiple scenario trees, we construct confidence ellipsoids around representative solutions, and present them to the DM for her/him to make a choice. With each iteration of the approach, an increasingly concentrated set of ellipsoids around the DM’s choices are generated. The procedure is demonstrated with tests performed using stocks traded on Borsa Istanbul.