|
| |
|
|
Ito formula and its applications
Till, Alexander ; Haman, Jiří (advisor) ; Maslowski, Bohdan (referee)
Title: Itô formula and its applications Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Jiří Haman Supervisor's e-mail address: j.haman@seznam.cz Abstract: The bachelor thesis contains basis and elementary findings of stochastic analysis. It includes definition and properties of stochastic integral with Wiener process as an integrator, definition of stochastic integral with Itô process as an integrator, Itô formula for functions of time and Wiener process, Itô formula for functions of time and Itô process. These conclusions are used to solve certain examples. Keywords: Wiener process, Stochastic integral, Itô formula 1
|
|
| |
|
|
Ito formula and its applications
Till, Alexander ; Haman, Jiří (advisor) ; Maslowski, Bohdan (referee)
Title: Itô formula and its applications Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Jiří Haman Supervisor's e-mail address: j.haman@seznam.cz Abstract: The bachelor thesis contains basis and elementary findings of stochastic analysis. It includes definition and properties of stochastic integral with Wiener process as an integrator, definition of stochastic integral with Itô process as an integrator, Itô formula for functions of time and Wiener process, Itô formula for functions of time and Itô process. These conclusions are used to solve certain examples. Keywords: Wiener process, Stochastic integral, Itô formula 1
|
|
|
Paradoxes in Probability Theory
Rušin, Ján ; Haman, Jiří (advisor) ; Dostál, Petr (referee)
The Bachelor's thesis present an overview and description of selected probability theory paradoxes, namely the paradox of Monty Hall, the Bertrand's paradox and the St. Peterburg paradox. In every chapter the reader is at first apprised of the formulation and the essence of the paradox. Then we show some possible solutions of this paradox. In original formulation of Monty Hall paradox there exists just one solution which can be reached by using two different ways. We add also some simple modifications to this particular paradox. The formula- tion of Bertrand's paradox is ambiguous which we show by using four selected approaches. And very similar situation arises in St. Peterburg paradox which we resolve by using three different approaches. 1
|
|
|
Martingale measures and pricing of financial derivatives
Melicherčík, Martin ; Dostál, Petr (advisor) ; Haman, Jiří (referee)
Title: Martingale measures and pricing of financial derivatives Author: Martin Melicherčík Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Petr Dostál, Ph.D., Department of Probability and Mathema- tical Statistics Abstract: The theory written in this work explains basic tools for setting justified price of financial derivatives. Jusified pricing is based on principal of balance, which means, that in advance no side has bigger chance to profit than other. Because of this characteristic, the main pricing tool in the work are martingale measures, which respect the state of balance. From the point of view of martingale measures random processes keep their constant expected value, so we can never expect them to deflect to one side or another. The important part of the work, besides basics of martingales, is Douglas theorem, which answers the question of our ability to theoretically set the justified price of any financial derivative. In the last parts, there are also some manuals and examples how to determine the justified price. Keywords: martingale, martingale pricing, Douglas theorem, predictable process 1
|
|
| |
|
|
Applications of stochastic processes in finance
Haman, Jiří ; Beneš, Viktor (advisor) ; Dostál, Petr (referee)
In this thesis we consider a stochastic volatility model based on non-Gaussian Ornstein-Uhlenbeck process (see also Barndor -Nielsen and Shephard [1]) where the logarithm of an asset price is the solution of a stochastic di erential equation without drift. The volatility component is modelled as a stationary, latent Ornstein-Uhlenbeck process, driven by a non-Gaussian Lévy process. We perform Bayesian inference for model parameters by means of Markov chain Monte Carlo algorithm based on data augmentation. The algorithm corresponds to a standard hierarchical parametrization of the model. The aim of this thesis is to express the unobserved stochastic volatility process for observed asset price. The algorithm is applied to the simulated and real asset price where real asset price is US dollar (USD) - Pound sterling (GBP) exchange rate.
|
|
| |
|
| |
guest ::
RSS feed.