Stochastic programming requires the expression of uncertainty through scenarios. These scenarios represent the possible paths of stochastic elements which are generally represented by a continuous distribution or a discrete distribution with many outcomes. Hoyland and Wallace (2001) developed a nonlinear program for scenario generation based on the satisfaction of specified statistical properties. In this paper, we propose a goal programming model that allows the generation of a limited number of discrete scenarios for several random elements. The motivation of the scenario tree generation is to represent uncertainty for the stochastic portfolio selection. The obtained scenarios are utilized in a stochastic goal programming model that helps a decision maker (DM) choosing an efficient combination of assets. An illustrative example from the Tunisian stock market securities is provided. In this example, we consider random elements as the price, and the rate of return of each security.
Groupe d’études et de recherche en analyse des décisions