Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric

0583619 - ÚTIA 2024 RIV CZ eng C - Conference Paper (international conference)
Kaňková, Vlasta
Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric.
Proceedings of the 41st International Conference on Mathematical Methods in Econometrics. Praha: The Czech Society of Operations Research, 2023 - (Sekničková, J.; Holý, V.), s. 192-197. ISBN 978-80-11-04132-8. ISSN 2788-3965.
[MME 2023: Mathematical Methods in Economics /41./. Prague (CZ), 13.09.2023-15.09.2023]
R&D Projects: GA ČR GA18-02739S
Institutional support: RVO:67985556
Keywords : Stochastic optimization problems * static problems * empirical measure * point estimates * interval estimates * nonlinear dependence
OECD category: Economic Theory
http://library.utia.cas.cz/separaty/2023/E/kankova-0583619.pdf

Many economic and financial applications lead to deterministic optimization problems depending on a probability measure. It happens very often (in applications) that these problems have to be solved on the data base. Point estimates of an optimal value and estimates of an optimal solutionset can be obtained by this approach. A consistency, a rate of convergence and normal properties, of these estimates, have been discussed (many times) not only under assumptions of independent data corresponding to the distributions with light tails, but also for weak dependent data and the distributions with heavy tails. However, it is also possible to estimate (on the data base) a confidence intervals and bounds for the optimal value and the optimal solutions. To analyze this approach we focus on a special case of static problems depending nonlineary on the probability measure. Stability results based on the Wasserstein metric and the Valander approach will be employed for the above mentioned analysis.
Permanent Link: https://hdl.handle.net/11104/0351623