Multiobjective Stochastic Optimization Problems with Probability Constraints

Multiobjective optimization problems depending on a probability measure often correspond to situations in which an economic or financial process is simultaneously influenced by a random factor and a decision parameter. Moreover it is reasonable to evaluate the process by a few objective functions and it seems reasonable to determine the "decision" with respect to the mathematical expectation of objectives. Complete knowledge of the probability measure is a necessary condition to analyze the problem. However, in applications mostly the problem has to be solved on the data base. A relationship between "characteristics" obtained on the base of complete knowledge of the probability measure and those obtained on the above mentioned data base has been already investigated in the case when constraints set is not depending on the probability measure ([9], [10]). The aim of the work will be to try to relax this condition.