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Suitable utility function identification
Majerová, Michaela ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
At the beginning of this work we study basic properties of utility functions and connection between their shape and investor's relation to risk. Then we define risk premium and we recall measure of risk aversion. In the second chapter we study classification of utility functions according to the absolute risk aversion measure and we list some basic types of utility functions. In the third chapter we construct investor's utility function. We use values of insurance premium which we get from questionnaire filled by MFF UK students. We use these utility functions in the last chapter. First we define portfolio selection problem and then we find optimal portfolio for different investors.
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Robust portfolio selection problem
Zákutná, Tatiana ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
In this thesis, a portfolio optimization with integer variables which influ- ence optimal assets allocation, is studied. Measures of risk are defined and the cor- responding mean-risk models are derived. Two methods are used to develop robust models involving uncertainty in probability distribution: the worst-case analyses and contamination. The uncertainty in values of scenarios and in their probabili- ties of the discrete probability distribution is assumed separately followed by their combination. These models are applied to stock market data with using optimization software GAMS.
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Analysis of portfolio optimization models with probability constraints
Kaľatová, Monika ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
K ú ové slová: optimalizácia portfólia, pravdepodobnostné obmedzenie, anal˝za citlivosti Title: Analysis of portfolio optimization models with probability constraints Author: Monika Ka atová Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloö Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: This thesis focuses on analysis of optimization problems with proba- bility constraints which are used in the portfolio theory. Firstly, the notion of probability constraint, fundamental to this thesis, is established. Afterwards, we present assumptions describing situations, in which the feasible set with probabi- lity constraint is convex. We focus mainly on Telser's and Kataoka's models with individual probability constraint. Furthermore, we derive both of these models using the assumption of a given probabilistic distribution. In the empirical part Telser's and Kataoka's models are applied to financial data obtained from the Prague Stock Exchange. Keywords: portfolio optimization, chance constraints, sensitivity analysis iii
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Maximum Return Portfolio
Palko, Maximilián ; Večeř, Jan (advisor) ; Šmíd, Martin (referee)
Classical method of portfolio selection is based on minimizing the variabi- lity of the portfolio. The Law of Large Numbers tells us that in case of longer investment horizon it should be enough to invest in the asset with the highest expected return which will eventually outperform any other portfolio. In our thesis we will suggest some portfolio creation methods which will create Maxi- mum Return Portfolios. These methods will be based on finding the asset with maximal expected return. That way we will avoid the problem of estimation errors of expected returns. Two of those methods will be selected based on the results of simulation analysis. Those two methods will be tested with the real stock data and compared with the S&P 500 index. Results of the testing suggest that our portfolios could have an application in the real world. Mainly because our portfolios showed to be significantly better than the index in the case of 10 year investment horizon. 1
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Robust portfolio selection problem
Zákutná, Tatiana ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
In this thesis, a portfolio optimization with integer variables which influ- ence optimal assets allocation, is studied. Measures of risk are defined and the cor- responding mean-risk models are derived. Two methods are used to develop robust models involving uncertainty in probability distribution: the worst-case analyses and contamination. The uncertainty in values of scenarios and in their probabili- ties of the discrete probability distribution is assumed separately followed by their combination. These models are applied to stock market data with using optimization software GAMS.
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Suitable utility function identification
Majerová, Michaela ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
At the beginning of this work we study basic properties of utility functions and connection between their shape and investor's relation to risk. Then we define risk premium and we recall measure of risk aversion. In the second chapter we study classification of utility functions according to the absolute risk aversion measure and we list some basic types of utility functions. In the third chapter we construct investor's utility function. We use values of insurance premium which we get from questionnaire filled by MFF UK students. We use these utility functions in the last chapter. First we define portfolio selection problem and then we find optimal portfolio for different investors.
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