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Obchodní strategie v neúplném trhu
Bunčák, Tomáš ; Karlova, Andrea (advisor) ; Štěpán, Josef (referee)
MASTER THESIS ABSTRACT TITLE: Trading Strategy in Incomplete Market AUTHOR: Tomáš Bunčák DEPARTMENT: Department of Probability and Mathematical Statistics, Charles University in Prague SUPERVISOR: Andrea Karlová We focus on the problem of finding optimal trading strategies (in a meaning corresponding to hedging of a contingent claim) in the realm of incomplete markets mainly. Although various ways of hedging and pricing of contingent claims are outlined, main subject of our study is the so-called mean-variance hedging (MVH). Sundry techniques used to treat this problem can be categorized into two approaches, namely a projection approach (PA) and a stochastic control approach (SCA). We review the methodologies used within PA in diversely general market models. In our research concerning SCA, we examine the possibility of using the methods of optimal stochastic control in MVH, and we study the problem of our interest in several settings of market models; involving cases of pure diffusion models and a jump- diffusion case. In order to reach an exemplary comparison, we provide solutions of the MVH problem in the setting of the Heston model via techniques of both of the approaches. Some parts of the thesis are accompanied with numerical illustrations.
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Obchodní strategie v neúplném trhu
Bunčák, Tomáš ; Karlova, Andrea (advisor) ; Štěpán, Josef (referee)
MASTER THESIS ABSTRACT TITLE: Trading Strategy in Incomplete Market AUTHOR: Tomáš Bunčák DEPARTMENT: Department of Probability and Mathematical Statistics, Charles University in Prague SUPERVISOR: Andrea Karlová We focus on the problem of finding optimal trading strategies (in a meaning corresponding to hedging of a contingent claim) in the realm of incomplete markets mainly. Although various ways of hedging and pricing of contingent claims are outlined, main subject of our study is the so-called mean-variance hedging (MVH). Sundry techniques used to treat this problem can be categorized into two approaches, namely a projection approach (PA) and a stochastic control approach (SCA). We review the methodologies used within PA in diversely general market models. In our research concerning SCA, we examine the possibility of using the methods of optimal stochastic control in MVH, and we study the problem of our interest in several settings of market models; involving cases of pure diffusion models and a jump- diffusion case. In order to reach an exemplary comparison, we provide solutions of the MVH problem in the setting of the Heston model via techniques of both of the approaches. Some parts of the thesis are accompanied with numerical illustrations.
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Plně pravděpodobnostní návrh řízení pro gaussovské stochastické systémy
Belda, Květoslav ; Tesař, Ludvík
Control of stochastic systems is generally formulated as a minimization of expected value of a suitably chosen loss function of system inputs, outputs and desired behavior with respect to feedback control strategies. The standard strategies (e.g. Linear Quadratic Gaussian control) choose control actions that make the closed-loop behavior as close as possible to desired one using expected and desired output values. More general approach is to consider complex information on stochastic system behavior by complex probabilistic description. On this approach, fully probabilistic design is based. It uses probabilistic description for characterization of closed-loop of stochastic system and its desired behavior. This paper points out the basic principles of fully probabilistic design and its practical application to the control of Gaussian stochastic systems.
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Adaptivní řízení aplikované na data z finančních trhů
Šindelář, Jan ; Kárný, Miroslav
The article describes a formal approach to decision making optimization in commodity futures markets. We try to plan optimal decision at a given time to trade in the market. We use dynamic programming with loss function equal to the negative profit, where we estimate the PDFs of parameters using Bayesian learning. Parametrized models are chosen from exponential family and trading costs (slippage and commission) are taken into account. We support the theoretical results by a series of experiments.
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