|
|
Application of cooperative game theory in Cournot oligopoly
Eryganov, Ivan ; Mazal,, Jan (referee) ; Hrdina, Jaroslav (advisor)
This Master’s thesis deals with the application of cooperative game theory for solving the problems of Cournot's oligopolies. The knowledge of oligopoly theory and game theory has been elaborated to build a model describing the behavior of companies at a market that meets the preconditions of Cournot's oligopoly. The definition of cooperative game is based on the -characteristic function, which takes into account, compared to classical methods, that companies which are not in the coalition are pursuing their own profits, not suppressing coalition positions. The properties of the resulting cooperative games are examined in detail, focusing on monotony and convexity. Several theorems about these properties have been derived and their economic interpretations are given. Also, the question of calculation of the -characteristic function using the best-reply dynamics algorithm is being solved, and its convergence for a given type of games is justified. The model is applied to data from the oil market, which is further characterized by the results of the cooperative game.
|
|
|
Interest Rate Risk Analysis by Principal Component Method
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Prášková, Zuzana (referee)
Presented study analyzes interest rate risk associated with the possession of given fixed coupon bond. In the first chapter, we define some of the basic concepts and provide description of available data. These are historical data on spot interest rates of zero-coupon bonds for various times to maturity which will be used for the construction of the yield curves. Based on these bond yield curves we evaluate the bond, thus obtaining a picture of the evolution of its price. Later on, we try to estimate its price tomorrow. We present two approaches how to deal with this problem. First approach is the normal interest rate risk analysis based on duration and convexity, second approach is the method of principal components which will be applied to the historical daily changes in yield curves. The method of principal components is introduced in detail.
|
|
|
Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
1 Abstract: This thesis deals with chance constrained stochastic programming problems. We consider several chance constrained models and we focus on their convexity property. The thesis presents the theory of α-concave functions and measures as a basic tool for proving the convexity of the problems. We use the results of the theory to prove the convexity of the models first for the continu- ous distributions, then for the discrete distributions of the random vectors. We characterize a large class of the continuous distributions, that satisfy the suffi- cient conditions for the convexity of the given models and we present solving algorithms for these models. We present sufficient conditions for the convexity of the problems with dicrete distributions, too. We also deal with the algorithms for solving non-convex problems and briefly discuss the difficulties that can occur when using these methods.
|
|
|
Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
This thesis deals with chance constrained stochastic programming pro- blems. The first chapter is an introduction. We formulate several stochastic pro- gramming problems in the second chapter. In chapter 3 we present the theory of α-concave functions and measures as a basic tool for proving convexity of the problems formulated in chapter 2 for the continuous distributions of the random vectors. We use the results of the theory to characterize a large class of the conti- nuous distributions, that satisfy the sufficient conditions for the convexity and to prove convexity of concrete sets. In chapter 4 we present sufficient conditions for the convexity of the problems and we briefly discuss the method of the p-level ef- ficient points. In chapter 5 we solve a portfolio selection problem using Kataoka's model. 1
|
|
|
Application of cooperative game theory in Cournot oligopoly
Eryganov, Ivan ; Mazal,, Jan (referee) ; Hrdina, Jaroslav (advisor)
This Master’s thesis deals with the application of cooperative game theory for solving the problems of Cournot's oligopolies. The knowledge of oligopoly theory and game theory has been elaborated to build a model describing the behavior of companies at a market that meets the preconditions of Cournot's oligopoly. The definition of cooperative game is based on the -characteristic function, which takes into account, compared to classical methods, that companies which are not in the coalition are pursuing their own profits, not suppressing coalition positions. The properties of the resulting cooperative games are examined in detail, focusing on monotony and convexity. Several theorems about these properties have been derived and their economic interpretations are given. Also, the question of calculation of the -characteristic function using the best-reply dynamics algorithm is being solved, and its convergence for a given type of games is justified. The model is applied to data from the oil market, which is further characterized by the results of the cooperative game.
|
|
|
Gradient polyconvexity and its application to problems of mathematical elasticity and plasticity
Zeman, Jiří ; Kružík, Martin (advisor) ; Zeman, Jan (referee)
Polyconvexity is a standard assumption on hyperelastic stored energy densities which, together with some growth conditions, ensures the weak lower semicontinuity of the respective energy functional. The present work first reviews known results about gradient polyconvexity, introduced by Benešová, Kružík and Schlömerkemper in 2017. It is an alternative property to polyconvexity, better-suited e.g. for the modelling of shape-memory alloys. The principal result of this thesis is the extension of an elastic material model with gradient polyconvex energy functional to an elastoplastic body and proving the existence of an energetic solution to an associated rate- independent evolution problem, proceeding from previous work of Mielke, Francfort and Mainik. 1
|
|
|
Maximum likelihood theory for not i.i.d. observations
Kielkowská, Eva ; Omelka, Marek (advisor) ; Pešta, Michal (referee)
Maximum likelihood approach for independent but not identically distributed observations is studied. In the first part of the thesis, conditions for consistency and asymptotic normality of the maximum likelihood estimates for this case are stated. Uniform integrability has a major role in proving the desired properties. K-sample problem serves as an example for using the described method. The second part is focused on estimates obtained by minimizing convex functions. Convexity is a key for showing the consistency and asymptotic normality of the estimates in this case. The results can be used for maximum likelihood when observations with logconcave densities are involved. Finally, normal linear model, logistic regression and Poisson regression examples are provided to present the application of the method.
|
|
|
Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
This thesis deals with chance constrained stochastic programming pro- blems. The first chapter is an introduction. We formulate several stochastic pro- gramming problems in the second chapter. In chapter 3 we present the theory of α-concave functions and measures as a basic tool for proving convexity of the problems formulated in chapter 2 for the continuous distributions of the random vectors. We use the results of the theory to characterize a large class of the conti- nuous distributions, that satisfy the sufficient conditions for the convexity and to prove convexity of concrete sets. In chapter 4 we present sufficient conditions for the convexity of the problems and we briefly discuss the method of the p-level ef- ficient points. In chapter 5 we solve a portfolio selection problem using Kataoka's model. 1
|
|
|
Interest Rate Risk Analysis by Principal Component Method
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Prášková, Zuzana (referee)
Presented study analyzes interest rate risk associated with the possession of given fixed coupon bond. In the first chapter, we define some of the basic concepts and provide description of available data. These are historical data on spot interest rates of zero-coupon bonds for various times to maturity which will be used for the construction of the yield curves. Based on these bond yield curves we evaluate the bond, thus obtaining a picture of the evolution of its price. Later on, we try to estimate its price tomorrow. We present two approaches how to deal with this problem. First approach is the normal interest rate risk analysis based on duration and convexity, second approach is the method of principal components which will be applied to the historical daily changes in yield curves. The method of principal components is introduced in detail.
|
|
|
Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
1 Abstract: This thesis deals with chance constrained stochastic programming problems. We consider several chance constrained models and we focus on their convexity property. The thesis presents the theory of α-concave functions and measures as a basic tool for proving the convexity of the problems. We use the results of the theory to prove the convexity of the models first for the continu- ous distributions, then for the discrete distributions of the random vectors. We characterize a large class of the continuous distributions, that satisfy the suffi- cient conditions for the convexity of the given models and we present solving algorithms for these models. We present sufficient conditions for the convexity of the problems with dicrete distributions, too. We also deal with the algorithms for solving non-convex problems and briefly discuss the difficulties that can occur when using these methods.
|
guest ::
