Selecting stock portfolio using multi-objective stochastic programming and interval fuzzy numbers

Uncertainty problems related to a financial market are traditionally dealt with stochastic or fuzzy approaches. Comparing with fuzzy variables with complex distributionfunctions, intervals can be more easily operated. Thus it is a good alternative to formulate an optimization problem with an intervalmodel under some uncertain environment such as investment in a portfolio. This paper presents a decision support model called Interval Chance Constrained Goal Attainment Programming (ICCGAP) to optimize multi-objective portfolio decision problem under uncertainty. ICCGAP is a combination of the well-knownclassical approach of Chance Constrained programming (CCP) and A-priori multi-objective approach of Goal AttainmentProgramming (GAP) with interval fuzzy numbers. In ICCGAP, random variables are considered normally distributed with intervals means and known variances. Proposed model is illustrated by a multi-objective problem to select optimal portfolio in Iran stock exchange market under uncertainty. Results obtain under pessimistic and optimistic conditions of objectives.