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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.2019-11-17T09:52:28ZHow to be oriented in quality and no quality resources
https://dspace.tul.cz/handle/15240/154237
How to be oriented in quality and no quality resources
Zizienová, Marta
2019-01-01T00:00:00ZAdaptive wavelet based scheme for option pricing
https://dspace.tul.cz/handle/15240/154236
Adaptive wavelet based scheme for option pricing
Finěk, Václav
This contribution deals with the numerical solution of the Black-Scholes equation. The Crank-Nicolson scheme is applied for time discretization and wavelets are applied for space discretization. Hermite cubic spline wavelets with four vanishing moments are adaptively used because they enable higher order approximations, are well-conditioned, have short supports, have a high potential in adaptive methods due to the four vanishing wavelet moments and mainly because arising stiffness matrices are sparse in wavelet coordinates.
Due to irregularities of the initial data in the Black-Scholes model, the use of the second-order Crank-Nicolson scheme usually requires a certain amount of damping to compensate for the known weak stability of this scheme. We numerically show here that optimal convergence rate for a proposed adaptive wavelet discretization in space can be obtained without any damping and without any restriction on the time step. A numerical example is given for the Black-Scholes equation with real data from the Frankfurt Stock Exchange. We also compare numerical results for adaptive and non-adaptive wavelet discretization in space.
2018-01-01T00:00:00ZWavelet-Galerkin Method for Option Pricing under a Double Exponential Jump-Diffusion Model
https://dspace.tul.cz/handle/15240/154235
Wavelet-Galerkin Method for Option Pricing under a Double Exponential Jump-Diffusion Model
Černá, Dana
The paper is concerned with pricing European options using a double exponential jump-diffusion model proposed by Kou in 2002. The Kou model is represented by nonstationary partial integro-differential equation. We use the Crank-Nicolson scheme for semidiscretization in time and the Galerkin method with cubic spline wavelets for solving integro-differential equation at each time level. We show the decay of elements of the matrices arising from discretization of the integral term of the equation. Due to this decay the discretization matrices can be truncated and represented by quasi-sparse matrices while the most standard methods suffer from the fact that the discretization matrices are full. Since the basis functions are piecewise cubic we obtain a high order convergence and the problem can be resolved with the small number of degrees of freedom. We present a numerical example for a European put option and we compare the results with other methods.
2018-01-01T00:00:00ZControl of Jet Flow Angle in Continuous Casting Process using an Electromagnetic Brake
https://dspace.tul.cz/handle/15240/154234
Control of Jet Flow Angle in Continuous Casting Process using an Electromagnetic Brake
Abouelazayem, Shereen; Glavinic, Ivan; Wondrak, Thomas; Hlava, Jaroslav
The flow pattern in the mould of the continuous casting is an important factor in determining the quality of the steel slabs that are produced in the end of the process. Hence it can heavily influence manufacturing costs due to the scrap percentage. Electromagnetic actuators are frequently used in the continuous casting process to stabilize the flow in the mould and therefore produce higher quality of steel slabs. Usually they are used in open loop but their effect on the flow pattern may be much better directed if they are used as a part of closed loop control based on real time measurements. In this paper, a closed loop controller is proposed that adjusts the magnetic field of an electromagnetic brake using the real time measurement of the angle of the jet flowing from the Submerged Entry Nozzle (SEN). The angle is kept within a specific range by the controller in order to prevent a deeper jet impingement into the mould; this allows us to achieve the desirable double roll flow pattern, and to avoid the entrapment of slug. The controller is based on a model of the relationship between brake current and jet angle that was obtained using experimental data from a laboratory scale continuous casting plant.
2019-01-01T00:00:00Z