Scenario Generation and Empirical Estimation in Stochastic Optimization Problems: Survey and Open Questions

Vlasta Kaňková

Economic andf financial processes are mostly influenced by a random factor and
a decision parameter. The decision parameter can mostly be determined by an
optimization problem depending on the probability measure. In applications mostly
the decision parameter has to be obtained either on the data base (the underlying
distribution is replaced by empirical one) or by the problem with a simpler (mostly
discrete) distribution. In the both cases two problems correspond to the original
one: real and approximate. The relationship between them has been studied mostly
under "classical" assumptions: linear dependence on the measure, distributions with
thin tails, "classical" constraints sets, independent random sample, one-objective
problems and so on. Stability results have been mostly employed for it. An effort
has arisen to relax these assumptions. The aim is to give a survey of results for
these relaxed conditions, and to introduce problems waiting for solution.