Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates

0518579 - ÚTIA 2020 RIV CZ eng K - Conference Paper (Czech conference)
Kaňková, Vlasta
Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates.
Conference Proceedings. 37th International Conference on Mathematical Methods in Economics 2019. České Budějovice: University of South Bohemia in České Budějovice, Faculty of Economics, 2019 - (Houda, M.; Remeš, R.), s. 350-355. ISBN 978-80-7394-760-6.
[MME 2019: International Conference on Mathematical Methods in Economics /37./. České Budějovice (CZ), 11.09.2019-13.09.2019]
R&D Projects: GA ČR GA18-02739S
Institutional support: RVO:67985556
Keywords : Two-objective stochastic optimization problems * scalarization * stochastic dominance * empirical estimates
OECD category: Statistics and probability
http://library.utia.cas.cz/separaty/2019/E/kankova-0518579.pdf

Many economic and financial situations depend simultaneously on a random element and on a decision parameter. Mostly it is possible to influence the above mentioned situation by an optimization model depending on a probability measure. We focus on a special case of one-stage two objective stochastic “Mean-Risk problem”. Of course to determine optimal solution simultaneously with respect to the both criteria is mostly impossible. Consequently, it is necessary to employ some approaches. A few of them are known (from the literature), however two of them are very important: first of them is based on a scalarizing technique and the second one is based on the stochastic dominance. First approach has been suggested (in special case) by Markowitz, the second approach is based on the second order stochastic dominance. The last approach corresponds (under some assumptions) to partial order in the set of the utility functions.
The aim of the contribution is to deal with the both main above mentioned approaches. First, we repeat their properties and further we try to suggest possibility to improve the both values simultaneously with respect to the both criteria. However, we focus mainly on the case when probability characteristics has to be estimated on the data base.
Permanent Link: http://hdl.handle.net/11104/0303981