Multistage multivariate nested distance: An empirical analysis

Vitali, Sebastiano. "Multistage multivariate nested distance: An empirical analysis." Kybernetika 54.6 (2018): 1184-1200. <http://eudml.org/doc/294814>.

@article{Vitali2018,
abstract = {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.},
author = {Vitali, Sebastiano},
journal = {Kybernetika},
keywords = {multistage stochastic optimization; nested distance; portfolio models},
language = {eng},
number = {6},
pages = {1184-1200},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Multistage multivariate nested distance: An empirical analysis},
url = {http://eudml.org/doc/294814},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Vitali, Sebastiano
TI - Multistage multivariate nested distance: An empirical analysis
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 6
SP - 1184
EP - 1200
AB - 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.
LA - eng
KW - multistage stochastic optimization; nested distance; portfolio models
UR - http://eudml.org/doc/294814
ER -