- Code: I0459
- Unit Coordinator: Bruno Rubino
- ECTS Credits: 6
- Semester: 1
- Year: 1
- Campus: University of L'Aquila
- Language: English
- Aims:
The course is intended to introduce and develop an understanding of the concepts in nonlinear dynamical systems and bifurcation theory, and an ability to analyze nonlinear dynamic models of physical systems. The emphasis is to be on understanding the underlying basis of local bifurcation analysis techniques and their applications to structural and mechanical systems.
- Content:
Review of: first-order nonlinear ODE, first-order linear systems of autonomous ODE. Local theory for nonlinear dynamical systems: linearization, stable manifold theorem, stability and Liapunov functions, planar non-hyperbolic critical points, center manifold theory, normal form theory. Global theory for nonlinear systems: limit sets and attractors, limit cycles and separatrix cycles, Poincaré map. Hamiltonian systems. Poincaré-Bendixson theory. Bifurcation theory for nonlinear systems: structural stability, bifurcation at non-hyperbolic equilibrium points, Hopf bifurcations, bifurcation at non hyperbolic periodic orbits. Applications.
- Pre-requisites:
Ordinary differential equations
- Reading list:
Lawrence Perko, Differential equations and dynamical systems, Springer-Verlag, 2001
- Unit Coordinator: dr hab. Henryk Gacki, prof. PŚ
- ECTS Credits: 5
- Year: 2
- Campus: Silesian University of Technology
- Language: English
- Aims:
Introduction to the concept of independence of probabilistic objects.
The gamma distribution: basic properties and applications
- Content:
- The gamma distribution: basic properties and applications.- Metrics and norms in the space of measures.- Kantorovich-Rubinstein duality theorem.- Markov operators - properties and applications.- Invariant principle.- Lasota's theorem - Lower bounded technique.- Poisson driven stochastic differential equation.
- ECTS Credits: 4
- Semester: 2
- Year: 2
- Campus: Gdansk University of Technology
- Language: English
- Unit Coordinator: Pavel Popela
- ECTS Credits: 4
- Semester: 1
- Year: 2
- Campus: Brno University of Technology
- Language: English
- Aims:
1. Basic concepts, money, capital and securities.
2. Simple and compound interest rate, discounting.
3. Investments, cash lows and its measures, time value of money.
4. Assets and liabilities, insurance.
5. Bonds, options, futures, and forwards.
6. Exchange rates, inlation, indices.
7. Portfolio optimization - classical model.
8. Postoptimization, risk, funds.
9. Twostage models in finance.
10. Multistage models in finance.
11. Scenarios in financial mathematics.
12. Modelling principles, identification of dynamic data.
13. Discussion on advanced stochastic models.
- Content:
The basic concepts and models of financial problems are accompanied by the theory and simple examples.
- Pre-requisites:
The knowledge of Calculus and Linear Algebra together with probabilistic and statistical methods (including time series) as well as optimisation techniques within the framework of SOP and SO2 courses is required.
- Reading list:
1. Dupačová,J. et al.: Stochastic Models for Economics and Finance, Kluwer, 2003.
- Additional info:
The course presents basic financial models. It focuses on main concepts and computational methods.
Several lectures are especially developed to make students familiar with optimization models.
