16,471 research outputs found
Robustní metody v teorii portfolia
01 Abstrakt: Práca sa zaoberá robustnými metódami v teórii portfólia. Sú popísané rôzne miery rizika, ktoré sa využívajú pri optimalizácii portfólia, a na základe popísaných mier sú sformulované odpovedajúce optimalizačné úlohy. Analytické riešenie problému robustnej optimalizácie portfólia je uvedené pre miery rizika lower partial moments (LPM), value-at-risk (VaR) a conditional value-at-risk (CVaR). Práca popisuje aplikácie worst-case conditional value- at-risk (WCVaR) v oblasti finančného manažmentu, pričom sú detailnejšie skúmané a popísané minimalizačné úlohy za predpokladu zmiešaného rozdelenia, "box" neistoty a "ellipsoidal" neistoty. V závere práce sú prezentované výsledky numerickej štúdie na reálnych dátach z finančného trhu.01 Abstract: This thesis is concerned with the robust methods in portfolio theory. Different risk measures used in portfolio management are introduced and the corresponding robust portfolio optimization problems are formulated. The analytical solutions of the robust portfolio optimization problem with the lower partial moments (LPM), value-at-risk (VaR) or conditional value-at-risk (CVaR), as a risk measure, are presented. The application of the worst-case conditional value-at-risk (WCVaR) to robust portfolio management is proposed. This thesis considers WCVaR in the situation where only partial information on the underlying probability distribution is available. The minimization of WCVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. Several numerical examples based on real market data are presented to illustrate the proposed approaches and advantage of the robust formulation over the corresponding nominal approach.Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyMatematicko-fyzikální fakultaFaculty of Mathematics and Physic
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Data-Driven Robust Optimization
The last decade witnessed an explosion in the availability of data for
operations research applications. Motivated by this growing availability, we
propose a novel schema for utilizing data to design uncertainty sets for robust
optimization using statistical hypothesis tests. The approach is flexible and
widely applicable, and robust optimization problems built from our new sets are
computationally tractable, both theoretically and practically. Furthermore,
optimal solutions to these problems enjoy a strong, finite-sample probabilistic
guarantee. \edit{We describe concrete procedures for choosing an appropriate
set for a given application and applying our approach to multiple uncertain
constraints. Computational evidence in portfolio management and queuing confirm
that our data-driven sets significantly outperform traditional robust
optimization techniques whenever data is available.Comment: 38 pages, 15 page appendix, 7 figures. This version updated as of
Oct. 201
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