Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00502907" target="_blank" >RIV/67985556:_____/18:00502907 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.14736/kyb-2018-6-1231" target="_blank" >http://dx.doi.org/10.14736/kyb-2018-6-1231</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14736/kyb-2018-6-1231" target="_blank" >10.14736/kyb-2018-6-1231</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

Popis výsledku v původním jazyce

Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e.g. problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem U of the utility functions. Especially, considering U = U_1 (where U_ is a system of a non decreasing concave nonnegative utility functions) we obtain second order stochastic dominance constraints. Unfortunately it is also known that these problems are rather complicated as from the theoretical and the numerical point of view. Moreover, these problems go to semi-infinite optimization problems for which Slater's condition is not necessary fulfilled. Consequently it is suitable to modify the constraints. A question arises how to do it. The aim of the paper is to suggest one of the possibilities how to modify the original problem with an „estimation“ of a gap between the original and modified problem. To this end the stability results obtained on the base of the Wasserstein metric corresponding to L_1 norm are employed. Moreover, we mention a scenario generation and an investigation of empirical estimates. At the end attention will be paid to heavy tailed distributions.

Název v anglickém jazyce

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

Popis výsledku anglicky

Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e.g. problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem U of the utility functions. Especially, considering U = U_1 (where U_ is a system of a non decreasing concave nonnegative utility functions) we obtain second order stochastic dominance constraints. Unfortunately it is also known that these problems are rather complicated as from the theoretical and the numerical point of view. Moreover, these problems go to semi-infinite optimization problems for which Slater's condition is not necessary fulfilled. Consequently it is suitable to modify the constraints. A question arises how to do it. The aim of the paper is to suggest one of the possibilities how to modify the original problem with an „estimation“ of a gap between the original and modified problem. To this end the stability results obtained on the base of the Wasserstein metric corresponding to L_1 norm are employed. Moreover, we mention a scenario generation and an investigation of empirical estimates. At the end attention will be paid to heavy tailed distributions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA18-02739S" target="_blank" >GA18-02739S: Stochastická optimalizace v ekonomických procesech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Kybernetika

ISSN

0023-5954

e-ISSN

—

Svazek periodika

54

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

16

Strana od-do

1231-1246

Kód UT WoS článku

000457070200010

EID výsledku v databázi Scopus

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