Extended scenario analysis

Scenario analysis, as proposed by Rockafellar and Wets, in a stochastic programming technique employing discrete scenarios with known probabilities, usually covering several time periods. The requirement of nonanticipativity (not using future information to make present decisions) is enforced during the computational solution by using Spingarn’s method of partial inverses. The scenario analysis method as proposed relies on separability (with respect to scenarios) of all problem elements except the nonanticipativity constraint. The paper shows how, by making a little more use of the partial inverse technique, one can include nonseparable convex constraints in such a procedure. As an illustrative example, it shows how to analyze a portfolio optimization problem of Markowitz type (minimize variance for a given return) using scenarios. This offers the prospect of extending classical portfolio analysis from models based on historical behavior to models incorporating future scenarios of any desired type.