In this thesis we study models, which search for an optimal portfolio from a set of stocks. On the contrary to the classical approach focusing only on expected return and variance, we examine models where an additional crite- rion of skewness is included. Furthermore we formulate a model for measuring performance of a portfolio defined as the distance from the Pareto efficient frontier. In numerical experiments we apply the models on historical prices and stock data from the electronic stock market NASDAQ. We analyze the stock data from companies listed in the index NASDAQ-100. We conclude by comparing of optimal portfolios created using different models among each other, with trivial single-stock portfolios and the with NASDAQ-100 index itself.

Title: Almost stochastic dominance Author: Adam Štefánik Department: Probability and Mathematical Statistics Supervisor: RNDr. Ing. Miloš Kopa, PhD. Department of Probability and Mathematical Statistics, MFF UK Abstract: In the presented work we study the almost stochastic dominance and it's properties. Almost stochastic dominance is a relaxation of stochastic dominance. Almost stochastic dominance also deals with paradox situations occurring in case of stochastic dominance. This is a situation when stochastic dominance determines indifferent relation- ship between two portfolios, but in fact almost all investors can choose the better one. The original almost stochastic dominance presented by Leshno and Levy (2002) is compu- tationally expensive. Lizyayev and Ruszczy'nski (2012) suggested an alternative approach. This work introduces both approaches. The most interesting part of this work is a search for efficient portfolio with respect to the almost stochastic dominance by the simple linear programming. Lizyayev and Ruszczy'nski (2012) approach is applied to Kopa and Chovanec (2008) quantile approach for portfolio efficiency testing with respect to second order stochastic dominance. Keywords: almost stochastic dominance, efficiency, CVaR

At the beginning of this thesis we discuss DEA methods, which measure efficiency of Decision Making Units by comparing weighted inputs and outputs. First we describe basic DEA models without random inputs and outputs then stochastic DEA models which are derived from the deterministic ones. We describe more approaches to stochastic DEA models, for example using scenario approach or chance constrained programming problems. Another approach for measuring efficiency employs stochastic dominance. Stochastic dominance is a relation that allows to compare two random variables. We describe the first and second order stochastic dominance. First we consider pairwise stochastic efficiency, then we discuss the first and second order stochastic dominance portfolio efficiency. We describe different tests to measure this type of efficiency. At the end of this thesis we study efficiency of US stock portfolios using real historical data and we compare results obtained when using stochastic DEA models and stochastic dominance. Powered by TCPDF (www.tcpdf.org)

The thesis deals with high-order stochastic dominance of random variables and portfolios. The summary of findings about high-order stochastic dominance and portfolio efficiency is presented. As a main part of the thesis it is proven that under assumption of both normal and gamma distribution the infinite-order stochastic dominance is equivalent to the second-order stochastic dominance. The necessary and sufficient condition for the infinite-order stochastic dominance portfolio efficiency is derived under the assumption of normality. The condition is used in the empirical part of the thesis where parametrical approach to the portfolio efficiency is compared to the nonparametric scenario approach. The derived necessary and sufficient condition is based on the assumption of normality; therefore we use two sets of data, one with fulfilled assumption of normality and the other for which the assumption of normality was unambigously rejected. Consequently, the influence of fulfillment of the normality assumption on the results of the necessary and sufficient condition for portfolio efficiency is estimated.

Title: Semi-infinite programming: theory and portfolio efficiency application Author: Bc. Lukáš Klouda Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Miloš Kopa, PhD. Supervisor's e-mail address: kopa@karlin.mff.cuni.cz Abstract: The thesis deals with application of semi-infinite programming to a portfolio efficiency testing. The summary of semi-infinite programming, first and second order optimality conditions and duality in linear semi-infinite programming is presented. The optimization problem for a portfolio efficiency testing with respect to the second order stochastic dominance under assumption of discrete, normal, Students and general elliptical distribution is formulated. Conditional value at risk(CVaR) is used as the risk measure, because of its consistency with the second order stochastic dominance relation. Efficiency of index PX with respect to the second order stochastic dominance is tested. The tests are performed using the program GAMS.

Made available in DSpace on 2014-12-17T13:56:59Z (GMT). No. of bitstreams: 1 SilvanaRNGS.pdf: 1357221 bytes, checksum: 35bf1743d1d55e62f648d7333de4412b (MD5) Previous issue date: 2009-02-26 / This research consists in studying the influence of the various type of construction systems of roofs with their energy efficiency as well as on the cost benefit for the commercial buildings on the temperatures condition of the city of Natal/RN. The main goal of this research is to analyze the cost benefit of the construction systems of roofs available on the market, taking into consideration the energy efficiency of the commercial buildings artificially air conditioned in order to be used by the projectors and to be adequated to the temperatures condition of the city of Natal/RN. The method of valuation of the cost benefit of roof systems consists in six steps: Features and simulation of the reference building; Analyze of sensitivity; Analyzes, features and simulation of alternatives of roof construction systems; Analyze of the cost of implementation; Analyze of the benefits of the alternatives comparing to the base case; And finally the analyze of the cost benefit. The model type chosen as reference was stores with pre molded buildings and system of roof with fiber ciment and ceiling . The thermal results showed the influence of the roof system on the energy efficiency of the building. The Final results of the simulations of the alternatives comes to a conclusion that the absortance is the variable that presents the best cost benefit relation and the reduction on the thermal transmittance still has limitations because of the high cost / Esta pesquisa aborda a influ?ncia de diversos tipos de sistemas construtivos de cobertas no desempenho energ?tico e na rela??o custo-benef?cio de edifica??es do tipo comercial para as condi??es clim?ticas da cidade do Natal/RN. O objetivo geral da pesquisa ? analisar a rela??o custo-beneficio de sistemas construtivos de cobertas dispon?veis no mercado, levando-se em considera??o o desempenho energ?tico de edifica??es comerciais climatizadas artificialmente, visando o seu uso por projetistas e que seja adequado ?s condi??es clim?ticas da cidade de Natal/RN. O m?todo de avalia??o do custo-benef?cio de sistemas de coberta consiste de seis etapas: caracteriza??o e simula??o da edifica??o de refer?ncia; an?lise de sensitividade; levantamento, caracteriza??o e simula??o de alternativas de sistemas construtivos de cobertas; quantifica??o dos custos de implanta??o; quantifica??o dos benef?cios das alternativas em rela??o ao caso base; e an?lise das rela??es de custo-benef?cio. O modelo escolhido como refer?ncia corresponde a lojas com sistema de galp?o pr?-moldado, e sistema de coberta com fibrocimento e forro. Seu comportamento t?rmico demonstrou a influ?ncia do sistema de coberta no desempenho energ?tico da edifica??o. Os resultados das simula??es das alternativas demonstraram que a absort?ncia ? a vari?vel que apresenta a melhor rela??o custo-benef?cio, enquanto que a redu??o da transmit?ncia t?rmica ainda apresenta limita??es devido ao custo