Alexander Erdélyi
A delay differential equation model of oscillations of exchange rates
Vedúci diplomovej práce: Prof. RNDr. Pavol Brunovský, DrSc.

Diplomová práca obhájená na študijnom odbore
Ekonomická a finančná matematika
v roku 2003


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1 Introduction
    1.1 The proposed model

2 Retarded functional differential equations -- selected topics
    2.1 Initial value problem, general autonomous equation
    2.2 Linear autonomous RFDE
    2.3 Nonlinear autonomous RFDE
    2.4 Centre manifold analysis

3 Analysis of the model
    3.1 Existence, uniqueness and boundedness of the solution
    3.2 Characteristic equation -- location of the roots
    3.3 Centre manifold analysis
    3.4 Stability analysis -- Lyapunov's second method
    3.5 Conclusions

4 Numerical simulations
    4.1 Asymptotically stable trajectories, a<1
    4.2 The boundary point a=1
    4.3 Locally unstable trajectories, a>1
    4.4 Conclusions

5 Real data observations
    5.1 Case One -- Assumption of constant `natural' exchange rate
    5.2 Case Two -- `Natural' exchange rate estimated by linear regression
    5.3 Case Three -- `Natural' exchange rate estimated by MA technique
    5.4 Conclusions

6 Conclusions

Appendix

References


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Stránku pripravil: Daniel Ševčovič, Ústav aplikovanej matematiky, MFF UK,Bratislava