MULTISTAGE MULTIVARIATE NESTED DISTANCE: AN EMPIRICAL ANALYSIS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10401759" target="_blank" >RIV/00216208:11320/18:10401759 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ld1qo9ueCM" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ld1qo9ueCM</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14736/kyb-2018-6-1184" target="_blank" >10.14736/kyb-2018-6-1184</a>

Jazyk výsledku

angličtina

Název v původním jazyce

MULTISTAGE MULTIVARIATE NESTED DISTANCE: AN EMPIRICAL ANALYSIS

Popis výsledku v původním jazyce

Multistage stochastic optimization requires the definition and the generation of a discrete stochastic tree that represents the evolution of the uncertain parameters in time and space. The dimension of the tree is the result of a trade-off between the adaptability to the original probability distribution and the computational tractability. Moreover, the discrete approximation of a continuous random variable is not unique. The concept of the best discrete approximation has been widely explored and many enhancements to adjust and fix a stochastic tree in order to represent as well as possible the real distribution have been proposed. Yet, often, the same generation algorithm can produce multiple trees to represent the random variable. Therefore, the recent literature investigates the concept of distance between trees which are candidate to be adopted as stochastic framework for the multistage model optimization. The contribution of this paper is to compute the nested distance between a large set of multistage and multivariate trees and, for a sample of basic financial problems, to empirically show the positive relation between the tree distance and the distance of the corresponding optimal solutions, and between the tree distance and the optimal objective values. Moreover, we compute a lower bound for the Lipschitz constant that bounds the optimal value distance.

Název v anglickém jazyce

MULTISTAGE MULTIVARIATE NESTED DISTANCE: AN EMPIRICAL ANALYSIS

Popis výsledku anglicky

Multistage stochastic optimization requires the definition and the generation of a discrete stochastic tree that represents the evolution of the uncertain parameters in time and space. The dimension of the tree is the result of a trade-off between the adaptability to the original probability distribution and the computational tractability. Moreover, the discrete approximation of a continuous random variable is not unique. The concept of the best discrete approximation has been widely explored and many enhancements to adjust and fix a stochastic tree in order to represent as well as possible the real distribution have been proposed. Yet, often, the same generation algorithm can produce multiple trees to represent the random variable. Therefore, the recent literature investigates the concept of distance between trees which are candidate to be adopted as stochastic framework for the multistage model optimization. The contribution of this paper is to compute the nested distance between a large set of multistage and multivariate trees and, for a sample of basic financial problems, to empirically show the positive relation between the tree distance and the distance of the corresponding optimal solutions, and between the tree distance and the optimal objective values. Moreover, we compute a lower bound for the Lipschitz constant that bounds the optimal value distance.

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/GJ18-01781Y" target="_blank" >GJ18-01781Y: Dynamické a granulární rezervování škod s využitím kopulí - DaGLoRCo</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

17

Strana od-do

1184-1200

Kód UT WoS článku

000457070200007

EID výsledku v databázi Scopus

2-s2.0-85064192757