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Original title:
Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric
Authors: Kaňková, Vlasta
Document type: Papers
Conference/Event: MME 2023: Mathematical Methods in Economics /41./, Prague (CZ), 20230913
Year: 2023
Language: eng
Abstract: 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.
Keywords: empirical measure; interval estimates; nonlinear dependence; point estimates; static problems; Stochastic optimization problems
Project no.: GA18-02739S (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 41st International Conference on Mathematical Methods in Econometrics, ISBN 978-80-11-04132-8, ISSN 2788-3965
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2023/E/kankova-0583619.pdf
Original record: https://hdl.handle.net/11104/0351623
Permalink: http://www.nusl.cz/ntk/nusl-541554
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Authors: Kaňková, Vlasta
Document type: Papers
Conference/Event: MME 2023: Mathematical Methods in Economics /41./, Prague (CZ), 20230913
Year: 2023
Language: eng
Abstract: 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.
Keywords: empirical measure; interval estimates; nonlinear dependence; point estimates; static problems; Stochastic optimization problems
Project no.: GA18-02739S (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 41st International Conference on Mathematical Methods in Econometrics, ISBN 978-80-11-04132-8, ISSN 2788-3965
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2023/E/kankova-0583619.pdf
Original record: https://hdl.handle.net/11104/0351623
Permalink: http://www.nusl.cz/ntk/nusl-541554
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Record created 2024-03-10, last modified 2024-04-15