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Random approximations in multiobjective programming - with an application to portfolio optimization with shortfall constraints

Vogel S.

Control and Cybernetics

1999

Vol. 28, no 4

703-724

Decision makers often heave to deal with a programming problem vhere some of the quantities are unknown. They will usually estimate these quantities and solve the problem as it then appears - the "approximate problem". Thus, there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. The paper summarizes such results for multiobjective programming problems. The results ase illustrated by means of the Markowitz model of portfolio optimization. In order to show how probabilistic constraints may be dealt with using this framework, a shortfall constraint is taken into account.