Encompassing statistically unquantifiable randomness in goal programming: an application to portfolio selection

Random events make multiobjective programming solutions vulnerable to changes in input data. In many cases statistically quantifiable information on variability of relevant parameters may not be available for decision making. This situation gives rise to the problem of obtaining solutions based on subjective beliefs and a priori risk aversion to random changes. To solve this problem, we propose to replace the traditional weighted goal programming achievement function with a new function that considers the decision maker’s perception of the randomness associated with implementing the solution through the use of a penalty term. This new function also implements the level of a priori risk aversion based around the decision maker’s beliefs and perceptions. The proposed new formulation is illustrated by means of a variant of the mean absolute deviation portfolio selection model. As a result, difficulties imposed by the absence of statistical information about random events can be encompassed by a modification of the achievement function to pragmatically consider subjective beliefs.