Kaiserslautern - Fachbereich Mathematik
Refine
Year of publication
- 2003 (13) (remove)
Document Type
- Doctoral Thesis (13) (remove)
Has Fulltext
- yes (13)
Keywords
- Navier-Stokes-Gleichung (2)
- Wavelet (2)
- Algebraische Geometrie (1)
- Archimedische Kopula (1)
- Asiatische Option (1)
- Basket Option (1)
- Biot-Savart Operator (1)
- Biot-Savart operator (1)
- Brownian motion (1)
- Brownsche Bewegung (1)
- CHAMP (1)
- Cauchy-Navier-Equation (1)
- Cauchy-Navier-Gleichung (1)
- Chi-Quadrat-Test (1)
- Cholesky-Verfahren (1)
- Deformationstheorie (1)
- Druckkorrektur (1)
- Elastische Deformation (1)
- Elliptische Verteilung (1)
- Erdmagnetismus (1)
- Expected shortfall (1)
- Extreme value theory (1)
- Filtergesetz (1)
- Finite-Volumen-Methode (1)
- Flachwasser (1)
- Flachwassergleichungen (1)
- Fourier-Transformation (1)
- Garbentheorie (1)
- Gruppenoperation (1)
- Heavy-tailed Verteilung (1)
- Hydrostatischer Druck (1)
- Immobilienaktie (1)
- Inverses Problem (1)
- Kopula <Mathematik> (1)
- Kreditrisiko (1)
- Lagrangian relaxation (1)
- Lineare Elastizitätstheorie (1)
- Marktrisiko (1)
- Martingaloptimalitätsprinzip (1)
- Mehrskalenanalyse (1)
- Modellbildung (1)
- Modulraum (1)
- Multivariate Wahrscheinlichkeitsverteilung (1)
- Nonparametric time series (1)
- Numerische Strömungssimulation (1)
- Oberflächenmaße (1)
- Optimierung (1)
- Optionsbewertung (1)
- Optionspreistheorie (1)
- Portfolio-Optimierung (1)
- Poröser Stoff (1)
- Quantile autoregression (1)
- Regularisierung (1)
- Riemannian manifolds (1)
- Riemannsche Mannigfaltigkeiten (1)
- Risikomanagement (1)
- SWARM (1)
- Scale function (1)
- Shallow Water Equations (1)
- Stochastische Processe (1)
- Tail Dependence Koeffizient (1)
- Value at Risk (1)
- Vektorkugelfunktionen (1)
- Vektorwavelets (1)
- Wavelet-Theorie (1)
- Wavelet-Theory (1)
- Wirbelabtrennung (1)
- Wirbelströmung (1)
- abgeleitete Kategorie (1)
- algebraic geometry (1)
- archimedean copula (1)
- asian option (1)
- basket option (1)
- derived category (1)
- elliptical distribution (1)
- flood risk (1)
- geomagnetism (1)
- group action (1)
- integer programming (1)
- martingale optimality principle (1)
- moduli space (1)
- multileaf collimator (1)
- multivariate chi-square-test (1)
- nonlinear term structure dependence (1)
- option pricing (1)
- portfolio-optimization (1)
- pressure correction (1)
- radiation therapy (1)
- sheaf theory (1)
- stochastic processes (1)
- subgradient (1)
- surface measures (1)
- tail dependence coefficient (1)
- toric geometry (1)
- torische Geometrie (1)
- vector spherical harmonics (1)
- vectorial wavelets (1)
- vertical velocity (1)
- vertikale Geschwindigkeiten (1)
- vortex seperation (1)
- Überflutung (1)
- Überflutungsrisiko (1)
Faculty / Organisational entity
Semiparametric estimation of conditional quantiles for time series, with applications in finance
(2003)
The estimation of conditional quantiles has become an increasingly important issue in insurance and financial risk management. The stylized facts of financial time series data has rendered direct applications of extreme value theory methodologies, in the estimation of extreme conditional quantiles, inappropriate. On the other hand, quantile regression based procedures work well in nonextreme parts of a given data but breaks down in extreme probability levels. In order to solve this problem, we combine nonparametric regressions for time series and extreme value theory approaches in the estimation of extreme conditional quantiles for financial time series. To do so, a class of time series models that is similar to nonparametric AR-(G)ARCH models but which does not depend on distributional and moments assumptions, is introduced. We discuss estimation procedures for the nonextreme levels using the models and consider the estimates obtained by inverting conditional distribution estimators and by direct estimation using Koenker-Basset (1978) version for kernels. Under some regularity conditions, the asymptotic normality and uniform convergence, with rates, of the conditional quantile estimator for strong mixing time series, are established. We study the estimation of scale function in the introduced models using similar procedures and show that under some regularity conditions, the scale estimate is weakly consistent and asymptotically normal. The application of introduced models in the estimation of extreme conditional quantiles is achieved by augmenting them with methods in extreme value theory. It is shown that the overal extreme conditional quantiles estimator is consistent. A Monte Carlo study is carried out to illustrate the good performance of the estimates and real data are used to demonstrate the estimation of Value-at-Risk and conditional expected shortfall in financial risk management and their multiperiod predictions discussed.
The present thesis deals with coupled steady state laminar flows of isothermal incompressible viscous Newtonian fluids in plain and in porous media. The flow in the pure fluid region is usually described by the (Navier-)Stokes system of equations. The most popular models for the flow in the porous media are those suggested by Darcy and by Brinkman. Interface conditions, proposed in the mathematical literature for coupling Darcy and Navier-Stokes equations, are shortly reviewed in the thesis. The coupling of Navier-Stokes and Brinkman equations in the literature is based on the so called continuous stress tensor interface conditions. One of the main tasks of this thesis is to investigate another type of interface conditions, namely, the recently suggested stress tensor jump interface conditions. The mathematical models based on these interface conditions were not carefully investigated from the mathematical point of view, and also their validity was a subject of discussions. The considerations within this thesis are a step toward better understanding of these interface conditions. Several aspects of the numerical simulations of such coupled flows are considered: -the choice of proper interface conditions between the plain and porous media -analysis of the well-posedness of the arising systems of partial differential equations; -developing numerical algorithm for the stress tensor jump interface conditions, coupling Navier-Stokes equations in the pure liquid media with the Navier-Stokes-Brinkman equations in the porous media; -validation of the macroscale mathematical models on the base of a comparison with the results from a direct numerical simulation of model representative problems, allowing for grid resolution of the pore level geometry; -developing software and performing numerical simulation of 3-D industrial flows, namely of oil flows through car filters.
The question of how to model dependence structures between financial assets was revolutionized since the last decade when the copula concept was introduced in financial research. Even though the concept of splitting marginal behavior and dependence structure (described by a copula) of multidimensional distributions already goes back to Sklar (1955) and Hoeffding (1940), there were very little empirical efforts done to check out the potentials of this approach. The aim of this thesis is to figure out the possibilities of copulas for modelling, estimating and validating purposes. Therefore we extend the class of Archimedean Copulas via a transformation rule to new classes and come up with an explicit suggestion covering the Frank and Gumbel family. We introduce a copula based mapping rule leading to joint independence and as results of this mapping we present an easy method of multidimensional chi²-testing and a new estimate for high dimensional parametric distributions functions. Different ways of estimating the tail dependence coefficient, describing the asymptotic probability of joint extremes, are compared and improved. The limitations of elliptical distributions are carried out and a generalized form of them, preserving their applicability, is developed. We state a method to split a (generalized) elliptical distribution into its radial and angular part. This leads to a positive definite robust estimate of the dispersion matrix (here only given as a theoretical outlook). The impact of our findings is stated by modelling and testing the return distributions of stock- and currency portfolios furthermore of oil related commodities- and LME metal baskets. In addition we show the crash stability of real estate based firms and the existence of nonlinear dependence in between the yield curve.