Kaiserslautern - Fachbereich Mathematik
Refine
Year of publication
Document Type
- Doctoral Thesis (292) (remove)
Has Fulltext
- yes (292)
Keywords
- Algebraische Geometrie (6)
- Portfolio Selection (6)
- Finanzmathematik (5)
- Optimization (5)
- Stochastische dynamische Optimierung (5)
- Elastizität (4)
- Homogenisierung <Mathematik> (4)
- Navier-Stokes-Gleichung (4)
- Numerische Mathematik (4)
- Portfolio-Optimierung (4)
- portfolio optimization (4)
- Bewertung (3)
- Computeralgebra (3)
- Erwarteter Nutzen (3)
- Finite-Volumen-Methode (3)
- Gröbner-Basis (3)
- Inverses Problem (3)
- Monte-Carlo-Simulation (3)
- Mosco convergence (3)
- NURBS (3)
- Numerische Strömungssimulation (3)
- Optionspreistheorie (3)
- Portfolio Optimization (3)
- Portfoliomanagement (3)
- Risikomanagement (3)
- Transaction Costs (3)
- Tropische Geometrie (3)
- Wavelet (3)
- isogeometric analysis (3)
- optimales Investment (3)
- Asymptotic Expansion (2)
- Asymptotik (2)
- B-Spline (2)
- B-splines (2)
- Derivat <Wertpapier> (2)
- Diskrete Fourier-Transformation (2)
- Elasticity (2)
- Endliche Geometrie (2)
- Erdmagnetismus (2)
- FFT (2)
- Filtergesetz (2)
- Filtration (2)
- Finite Pointset Method (2)
- Geometric Ergodicity (2)
- Hamilton-Jacobi-Differentialgleichung (2)
- Hochskalieren (2)
- IMRT (2)
- Isogeometrische Analyse (2)
- Kreditrisiko (2)
- Langevin equation (2)
- Lebensversicherung (2)
- Level-Set-Methode (2)
- Lineare Elastizitätstheorie (2)
- Lineare partielle Differentialgleichung (2)
- Local smoothing (2)
- Mathematik (2)
- Mehrskalenanalyse (2)
- Mehrskalenmodell (2)
- Mikrostruktur (2)
- Modulraum (2)
- Multiset Multicover (2)
- Partial Differential Equations (2)
- Partielle Differentialgleichung (2)
- Poröser Stoff (2)
- Regressionsanalyse (2)
- Regularisierung (2)
- Robust Optimization (2)
- Schnitttheorie (2)
- Statistisches Modell (2)
- Stochastic Control (2)
- Stochastische Differentialgleichung (2)
- Transaktionskosten (2)
- Upscaling (2)
- Vektorwavelets (2)
- White Noise Analysis (2)
- curve singularity (2)
- domain decomposition (2)
- duality (2)
- finite volume method (2)
- geomagnetism (2)
- homogenization (2)
- illiquidity (2)
- interface problem (2)
- mesh generation (2)
- optimal investment (2)
- regression analysis (2)
- splines (2)
- "Slender-Body"-Theorie (1)
- (Joint) chance constraints (1)
- 3D image analysis (1)
- A-infinity-bimodule (1)
- A-infinity-category (1)
- A-infinity-functor (1)
- ALE-Methode (1)
- Ableitungsfreie Optimierung (1)
- Adjoint method (1)
- Advanced Encryption Standard (1)
- Agriculture Loan (1)
- Algebraic dependence of commuting elements (1)
- Algebraic geometry (1)
- Algebraic groups (1)
- Algebraische Abhängigkeit der kommutierende Elementen (1)
- Algebraischer Funktionenkörper (1)
- Analysis (1)
- Angewandte Mathematik (1)
- Annulus (1)
- Anti-diffusion (1)
- Antidiffusion (1)
- Approximationsalgorithmus (1)
- Arbitrage (1)
- Arc distance (1)
- Archimedische Kopula (1)
- Asiatische Option (1)
- Asset allocation (1)
- Asset-liability management (1)
- Asympotic Analysis (1)
- Asymptotic Analysis (1)
- Asymptotische Entwicklung (1)
- Ausfallrisiko (1)
- Automorphismengruppe (1)
- Autoregressive Hilbertian model (1)
- Balance sheet (1)
- Barriers (1)
- Basic Scheme (1)
- Basis Risk (1)
- Basket Option (1)
- Bayes-Entscheidungstheorie (1)
- Beam models (1)
- Beam orientation (1)
- Bernstein–Gelfand–Gelfand construction (1)
- Beschichtungsprozess (1)
- Beschränkte Krümmung (1)
- Betrachtung des Schlimmstmöglichen Falles (1)
- Bilanzstrukturmanagement (1)
- Bildsegmentierung (1)
- Binomialbaum (1)
- Biorthogonalisation (1)
- Biot Poroelastizitätgleichung (1)
- Biot-Savart Operator (1)
- Biot-Savart operator (1)
- Boltzmann Equation (1)
- Bondindizes (1)
- Bootstrap (1)
- Boundary Value Problem / Oblique Derivative (1)
- Brinkman (1)
- Brownian Diffusion (1)
- Brownian motion (1)
- Brownsche Bewegung (1)
- CDO (1)
- CDS (1)
- CDSwaption (1)
- CFD (1)
- CHAMP (1)
- CPDO (1)
- Castelnuovo Funktion (1)
- Castelnuovo function (1)
- Cauchy-Navier-Equation (1)
- Cauchy-Navier-Gleichung (1)
- Censoring (1)
- Center Location (1)
- Change Point Analysis (1)
- Change Point Test (1)
- Change-point Analysis (1)
- Change-point estimator (1)
- Change-point test (1)
- Charakter <Gruppentheorie> (1)
- Chi-Quadrat-Test (1)
- Cholesky-Verfahren (1)
- Chow Quotient (1)
- Circle Location (1)
- Cluster-Analyse (1)
- Coarse graining (1)
- Cohen-Lenstra heuristic (1)
- Combinatorial Optimization (1)
- Commodity Index (1)
- Complex Structures (1)
- Composite Materials (1)
- Computer Algebra (1)
- Computer Algebra System (1)
- Computer algebra (1)
- Computeralgebra System (1)
- Conditional Value-at-Risk (1)
- Connectivity (1)
- Consistencyanalysis (1)
- Consistent Price Processes (1)
- Constraint Generation (1)
- Construction of hypersurfaces (1)
- Convergence Rate (1)
- Copula (1)
- Coupled PDEs (1)
- Coxeter-Freudenthal-Kuhn triangulation (1)
- Crash (1)
- Crash Hedging (1)
- Crash modelling (1)
- Crashmodellierung (1)
- Credit Default Swap (1)
- Credit Risk (1)
- Curvature (1)
- Curved viscous fibers (1)
- Cycle Decomposition (1)
- DSMC (1)
- Darstellungstheorie (1)
- Das Urbild von Ideal unter einen Morphismus der Algebren (1)
- Debt Management (1)
- Defaultable Options (1)
- Deformationstheorie (1)
- Degenerate Diffusion Semigroups (1)
- Delaunay (1)
- Delaunay triangulation (1)
- Delaunay triangulierung (1)
- Differential forms (1)
- Differenzenverfahren (1)
- Differenzmenge (1)
- Diffusion (1)
- Diffusion processes (1)
- Diffusionsprozess (1)
- Discriminatory power (1)
- Dispersionsrelation (1)
- Dissertation (1)
- Diversifikation (1)
- Druckkorrektur (1)
- Dünnfilmapproximation (1)
- EDF observation models (1)
- EM algorithm (1)
- Edwards Model (1)
- Effective Conductivity (1)
- Efficiency (1)
- Efficient Reliability Estimation (1)
- Effizienter Algorithmus (1)
- Effizienz (1)
- Eikonal equation (1)
- Elastische Deformation (1)
- Elastoplastizität (1)
- Elektromagnetische Streuung (1)
- Eliminationsverfahren (1)
- Elliptische Verteilung (1)
- Elliptisches Randwertproblem (1)
- Endliche Gruppe (1)
- Endliche Lie-Gruppe (1)
- Energy markets (1)
- Entscheidungsbaum (1)
- Entscheidungsunterstützung (1)
- Enumerative Geometrie (1)
- Erdöl Prospektierung (1)
- Erwartungswert-Varianz-Ansatz (1)
- Essential m-dissipativity (1)
- Expected shortfall (1)
- Exponential Utility (1)
- Exponentieller Nutzen (1)
- Extrapolation (1)
- Extreme Events (1)
- Extreme value theory (1)
- FEM (1)
- FPM (1)
- Faden (1)
- Fatigue (1)
- Feedfoward Neural Networks (1)
- Feynman Integrals (1)
- Feynman path integrals (1)
- Fiber suspension flow (1)
- Financial Engineering (1)
- Finanzkrise (1)
- Finanznumerik (1)
- Finite-Elemente-Methode (1)
- Finite-Punktmengen-Methode (1)
- Firmwertmodell (1)
- First Order Optimality System (1)
- Flachwasser (1)
- Flachwassergleichungen (1)
- Fluid dynamics (1)
- Fluid-Feststoff-Strömung (1)
- Fluid-Struktur-Kopplung (1)
- Fluid-Struktur-Wechselwirkung (1)
- Foam decay (1)
- Fokker-Planck-Gleichung (1)
- Forward-Backward Stochastic Differential Equation (1)
- Fourier-Transformation (1)
- Fredholmsche Integralgleichung (1)
- Functional autoregression (1)
- Functional time series (1)
- Funktionenkörper (1)
- GARCH (1)
- GARCH Modelle (1)
- Galerkin-Methode (1)
- Gamma-Konvergenz (1)
- Garantiezins (1)
- Garbentheorie (1)
- Gebietszerlegung (1)
- Gebietszerlegungsmethode (1)
- Gebogener viskoser Faden (1)
- Geo-referenced data (1)
- Geodesie (1)
- Geometrische Ergodizität (1)
- Gewichteter Sobolev-Raum (1)
- Gittererzeugung (1)
- Gleichgewichtsstrategien (1)
- Gradient based optimization (1)
- Granular flow (1)
- Granulat (1)
- Graph Theory (1)
- Gravitationsfeld (1)
- Gromov Witten (1)
- Gromov-Witten-Invariante (1)
- Große Abweichung (1)
- Gruppenoperation (1)
- Gruppentheorie (1)
- Gröbner bases (1)
- Gröbner-basis (1)
- Gyroscopic (1)
- Hadamard manifold (1)
- Hadamard space (1)
- Hadamard-Mannigfaltigkeit (1)
- Hadamard-Raum (1)
- Hamiltonian Path Integrals (1)
- Handelsstrategien (1)
- Harmonische Analyse (1)
- Harmonische Spline-Funktion (1)
- Hazard Functions (1)
- Heavy-tailed Verteilung (1)
- Hedging (1)
- Helmholtz Type Boundary Value Problems (1)
- Heston-Modell (1)
- Hidden Markov models for Financial Time Series (1)
- Hierarchische Matrix (1)
- Hilbert complexes (1)
- Homogenization (1)
- Homologische Algebra (1)
- Hub Location Problem (1)
- Hydrostatischer Druck (1)
- Hyperelastizität (1)
- Hyperelliptische Kurve (1)
- Hyperflächensingularität (1)
- Hyperspektraler Sensor (1)
- Hypocoercivity (1)
- Hysterese (1)
- ITSM (1)
- Idealklassengruppe (1)
- Illiquidität (1)
- Image restoration (1)
- Immiscible lattice BGK (1)
- Immobilienaktie (1)
- Index Insurance (1)
- Inflation (1)
- Infrarotspektroskopie (1)
- Insurance (1)
- Intensität (1)
- Internationale Diversifikation (1)
- Interpolation Algorithm (1)
- Inverse Problem (1)
- Irreduzibler Charakter (1)
- Isogeometric Analysis (1)
- Ito (1)
- Jacobigruppe (1)
- Kanalcodierung (1)
- Karhunen-Loève expansion (1)
- Kategorientheorie (1)
- Kelvin Transformation (1)
- Kirchhoff-Love shell (1)
- Kiyoshi (1)
- Kombinatorik (1)
- Kommutative Algebra (1)
- Konjugierte Dualität (1)
- Konstruktion von Hyperflächen (1)
- Kontinuum <Mathematik> (1)
- Kontinuumsphysik (1)
- Konvergenz (1)
- Konvergenzrate (1)
- Konvergenzverhalten (1)
- Konvexe Optimierung (1)
- Kopplungsmethoden (1)
- Kopplungsproblem (1)
- Kopula <Mathematik> (1)
- Kreitderivaten (1)
- Kryptoanalyse (1)
- Kryptologie (1)
- Krümmung (1)
- Kullback-Leibler divergence (1)
- Kurvenschar (1)
- LIBOR (1)
- Lagrangian relaxation (1)
- Laplace transform (1)
- Lattice Boltzmann (1)
- Lattice-BGK (1)
- Lattice-Boltzmann (1)
- Leading-Order Optimality (1)
- Least-squares Monte Carlo method (1)
- Level set methods (1)
- Lie algebras (1)
- Lie-Typ-Gruppe (1)
- Lippmann-Schwinger Equation (1)
- Lippmann-Schwinger equation (1)
- Liquidität (1)
- Locally Supported Zonal Kernels (1)
- Location (1)
- MBS (1)
- MKS (1)
- ML-estimation (1)
- Macaulay’s inverse system (1)
- Magneto-Elastic Coupling (1)
- Magnetoelastic coupling (1)
- Magnetoelasticity (1)
- Magnetostriction (1)
- Marangoni-Effekt (1)
- Market Equilibrium (1)
- Markov Chain (1)
- Markov Kette (1)
- Markov-Ketten-Monte-Carlo-Verfahren (1)
- Markov-Prozess (1)
- Marktmanipulation (1)
- Marktrisiko (1)
- Martingaloptimalitätsprinzip (1)
- Maschinelles Lernen (1)
- Mathematical Finance (1)
- Mathematics (1)
- Mathematische Modellierung (1)
- Mathematisches Modell (1)
- Matrixkompression (1)
- Matrizenfaktorisierung (1)
- Matrizenzerlegung (1)
- Maximal Cohen-Macaulay modules (1)
- Maximale Cohen-Macaulay Moduln (1)
- Maximum Likelihood Estimation (1)
- Maximum-Likelihood-Schätzung (1)
- Maxwell's equations (1)
- McKay conjecture (1)
- McKay-Conjecture (1)
- McKay-Vermutung (1)
- Mehrdimensionale Bildverarbeitung (1)
- Mehrdimensionales Variationsproblem (1)
- Mehrkriterielle Optimierung (1)
- Mehrskalen (1)
- Microstructure (1)
- Mie- and Helmholtz-Representation (1)
- Mie- und Helmholtz-Darstellung (1)
- Mikroelektronik (1)
- Mixed Connectivity (1)
- Mixed integer programming (1)
- Mixed method (1)
- Model-Dynamics (1)
- Modellbildung (1)
- Molekulardynamik (1)
- Momentum and Mas Transfer (1)
- Monte Carlo (1)
- Moreau-Yosida regularization (1)
- Morphismus (1)
- Multi Primary and One Second Particle Method (1)
- Multi-Asset Option (1)
- Multicriteria optimization (1)
- Multileaf collimator (1)
- Multiperiod planning (1)
- Multiphase Flows (1)
- Multiresolution Analysis (1)
- Multiscale modelling (1)
- Multiskalen-Entrauschen (1)
- Multispektralaufnahme (1)
- Multispektralfotografie (1)
- Multivariate Analyse (1)
- Multivariate Wahrscheinlichkeitsverteilung (1)
- Multivariates Verfahren (1)
- Networks (1)
- Netzwerksynthese (1)
- Neural Networks (1)
- Neuronales Netz (1)
- Nicht-Desarguessche Ebene (1)
- Nichtglatte Optimierung (1)
- Nichtkommutative Algebra (1)
- Nichtkonvexe Optimierung (1)
- Nichtkonvexes Variationsproblem (1)
- Nichtlineare Approximation (1)
- Nichtlineare Diffusion (1)
- Nichtlineare Optimierung (1)
- Nichtlineare Zeitreihenanalyse (1)
- Nichtlineare partielle Differentialgleichung (1)
- Nichtpositive Krümmung (1)
- Niederschlag (1)
- Nilpotent elements (1)
- No-Arbitrage (1)
- Non-commutative Computer Algebra (1)
- Nonlinear Optimization (1)
- Nonlinear time series analysis (1)
- Nonparametric time series (1)
- Nulldimensionale Schemata (1)
- Numerical Flow Simulation (1)
- Numerical methods (1)
- Numerische Mathematik / Algorithmus (1)
- Numerisches Verfahren (1)
- Oberflächenmaße (1)
- Oberflächenspannung (1)
- Optimal Control (1)
- Optimale Kontrolle (1)
- Optimale Portfolios (1)
- Optimierung (1)
- Optimization Algorithms (1)
- Option (1)
- Option Valuation (1)
- Optionsbewertung (1)
- Order (1)
- Ovoid (1)
- PDE-Constrained Optimization, Robust Design, Multi-Objective Optimization (1)
- POD (1)
- Papiermaschine (1)
- Parallel Algorithms (1)
- Paralleler Algorithmus (1)
- Partikel Methoden (1)
- Patchworking Methode (1)
- Patchworking method (1)
- Pathwise Optimality (1)
- Pedestrian FLow (1)
- Periodic Homogenization (1)
- Pfadintegral (1)
- Planares Polynom (1)
- Poisson noise (1)
- Poisson-Gleichung (1)
- PolyBoRi (1)
- Population Balance Equation (1)
- Portfolio Optimierung (1)
- Portfoliooptimierung (1)
- Preimage of an ideal under a morphism of algebras (1)
- Probust optimization (1)
- Projektionsoperator (1)
- Projektive Fläche (1)
- Prox-Regularisierung (1)
- Punktprozess (1)
- QMC (1)
- QVIs (1)
- Quadratischer Raum (1)
- Quantile autoregression (1)
- Quantization (1)
- Quasi-Variational Inequalities (1)
- RKHS (1)
- Radial Basis Functions (1)
- Radiotherapy (1)
- Randwertproblem (1)
- Randwertproblem / Schiefe Ableitung (1)
- Rank test (1)
- Rarefied gas (1)
- Reflexionsspektroskopie (1)
- Regime Shifts (1)
- Regime-Shift Modell (1)
- Regularisierung / Stoppkriterium (1)
- Regularization / Stop criterion (1)
- Regularization methods (1)
- Reliability (1)
- Restricted Regions (1)
- Riemannian manifolds (1)
- Riemannsche Mannigfaltigkeiten (1)
- Rigid Body Motion (1)
- Risikoanalyse (1)
- Risikomaße (1)
- Risikotheorie (1)
- Risk Management (1)
- Risk Measures (1)
- Risk Sharing (1)
- Robust smoothing (1)
- Rohstoffhandel (1)
- Rohstoffindex (1)
- Räumliche Statistik (1)
- SWARM (1)
- Sandwiching algorithm (1)
- Scale function (1)
- Schaum (1)
- Schaumzerfall (1)
- Schiefe Ableitung (1)
- Schwache Formulierung (1)
- Schwache Konvergenz (1)
- Schwache Lösu (1)
- Second Order Conditions (1)
- Semi-Markov-Kette (1)
- Semi-infinite optimization (1)
- Sequenzieller Algorithmus (1)
- Serre functor (1)
- Shallow Water Equations (1)
- Shape optimization (1)
- Simulation (1)
- Singular <Programm> (1)
- Singularity theory (1)
- Singularität (1)
- Singularitätentheorie (1)
- Slender body theory (1)
- Sobolev spaces (1)
- Sobolev-Raum (1)
- Solvency II (1)
- Solvency-II-Richtlinie (1)
- Spannungs-Dehn (1)
- Spatial Statistics (1)
- Spectral Method (1)
- Spectral theory (1)
- Spektralanalyse <Stochastik> (1)
- Spherical Fast Wavelet Transform (1)
- Spherical Location Problem (1)
- Sphärische Approximation (1)
- Spline-Approximation (1)
- Split Operator (1)
- Splitoperator (1)
- Sprung-Diffusions-Prozesse (1)
- Stabile Vektorbundle (1)
- Stable vector bundles (1)
- Standard basis (1)
- Standortprobleme (1)
- Statistics (1)
- Steuer (1)
- Stochastic Impulse Control (1)
- Stochastic Processes (1)
- Stochastic optimization (1)
- Stochastische Inhomogenitäten (1)
- Stochastische Processe (1)
- Stochastische Zinsen (1)
- Stochastische optimale Kontrolle (1)
- Stochastischer Prozess (1)
- Stochastisches Modell (1)
- Stokes-Gleichung (1)
- Stop- und Spieloperator (1)
- Stornierung (1)
- Stoßdämpfer (1)
- Strahlentherapie (1)
- Strahlungstransport (1)
- Structural Reliability (1)
- Strukturiertes Finanzprodukt (1)
- Strukturoptimierung (1)
- Strömungsdynamik (1)
- Strömungsmechanik (1)
- Subset Simulationen (1)
- Success Run (1)
- Survival Analysis (1)
- Systemidentifikation (1)
- Sägezahneffekt (1)
- Tail Dependence Koeffizient (1)
- Temporal Variational Autoencoders (1)
- Test for Changepoint (1)
- Thermophoresis (1)
- Thin film approximation (1)
- Tichonov-Regularisierung (1)
- Time Series (1)
- Time-Series (1)
- Time-delay-Netz (1)
- Topologieoptimierung (1)
- Topology optimization (1)
- Traffic flow (1)
- Transaction costs (1)
- Trennschärfe <Statistik> (1)
- Tropical Grassmannian (1)
- Tropical Intersection Theory (1)
- Tube Drawing (1)
- Two-Scale Convergence (1)
- Two-phase flow (1)
- Unreinheitsfunktion (1)
- Untermannigfaltigkeit (1)
- Upwind-Verfahren (1)
- Usage modeling (1)
- Utility (1)
- Value at Risk (1)
- Value at risk (1)
- Value-at-Risk (1)
- Variational autoencoders (1)
- Variationsrechnung (1)
- Vectorfield approximation (1)
- Vektorfeldapproximation (1)
- Vektorkugelfunktionen (1)
- Verschwindungsatz (1)
- Versicherung (1)
- Viskoelastische Flüssigkeiten (1)
- Viskose Transportschemata (1)
- Volatilität (1)
- Volatilitätsarbitrage (1)
- Vorkonditionierer (1)
- Vorwärts-Rückwärts-Stochastische-Differentialgleichung (1)
- Water reservoir management (1)
- Wave Based Method (1)
- Wavelet-Theorie (1)
- Wavelet-Theory (1)
- Weißes Rauschen (1)
- White Noise (1)
- Wirbelabtrennung (1)
- Wirbelströmung (1)
- Wissenschaftliches Rechnen (1)
- Worst-Case (1)
- Wärmeleitfähigkeit (1)
- Yaglom limits (1)
- Zeitintegrale Modelle (1)
- Zeitreihe (1)
- Zentrenprobleme (1)
- Zero-dimensional schemes (1)
- Zopfgruppe (1)
- Zufälliges Feld (1)
- Zweiphasenströmung (1)
- abgeleitete Kategorie (1)
- adaptive algorithm (1)
- algebraic attack (1)
- algebraic correspondence (1)
- algebraic function fields (1)
- algebraic geometry (1)
- algebraic number fields (1)
- algebraic topology (1)
- algebraische Korrespondenzen (1)
- algebraische Topologie (1)
- algebroid curve (1)
- alternating minimization (1)
- alternating optimization (1)
- analoge Mikroelektronik (1)
- angewandte Mathematik (1)
- angewandte Topologie (1)
- anisotropen Viskositätsmodell (1)
- anisotropic viscosity (1)
- applied mathematics (1)
- arbitrary Lagrangian-Eulerian methods (ALE) (1)
- archimedean copula (1)
- asian option (1)
- asymptotic-preserving (1)
- auto-pruning (1)
- basket option (1)
- benders decomposition (1)
- bending strip method (1)
- binomial tree (1)
- blackout period (1)
- bocses (1)
- boundary value problem (1)
- canonical ideal (1)
- canonical module (1)
- changing market coefficients (1)
- characteristic polynomial (1)
- closure approximation (1)
- clustering (1)
- clustering methods (1)
- combinatorics (1)
- composites (1)
- computational finance (1)
- computer algebra (1)
- computeralgebra (1)
- convergence behaviour (1)
- convex constraints (1)
- convex optimization (1)
- correlated errors (1)
- coupling methods (1)
- crash (1)
- crash hedging (1)
- credit risk (1)
- curvature (1)
- decision support (1)
- decision support systems (1)
- decoding (1)
- default time (1)
- degenerations of an elliptic curve (1)
- dense univariate rational interpolation (1)
- derived category (1)
- determinant (1)
- diffusion models (1)
- discrepancy (1)
- diversification (1)
- domain parametrization (1)
- double exponential distribution (1)
- downward continuation (1)
- efficiency loss (1)
- elastoplasticity (1)
- elliptical distribution (1)
- endomorphism ring (1)
- enumerative geometry (1)
- equilibrium strategies (1)
- equisingular families (1)
- face value (1)
- fiber reinforced silicon carbide (1)
- fibre lay-down dynamics (1)
- filtration (1)
- financial mathematics (1)
- finite difference schemes (1)
- finite element method (1)
- finite groups of Lie type (1)
- finite spin group (1)
- first hitting time (1)
- float glass (1)
- flood risk (1)
- fluid structure (1)
- fluid structure interaction (1)
- fluid-structure interaction (FSI) (1)
- forward-shooting grid (1)
- free surface (1)
- freie Oberfläche (1)
- gebietszerlegung (1)
- generic character table (1)
- gitter (1)
- glioblastoma (1)
- good semigroup (1)
- graph p-Laplacian (1)
- gravitation (1)
- group action (1)
- groups of Lie type (1)
- großer Investor (1)
- haptotaxis (1)
- hedging (1)
- heuristic (1)
- hierarchical matrix (1)
- hyperbolic systems (1)
- hyperelliptic function field (1)
- hyperelliptische Funktionenkörper (1)
- hyperspectal unmixing (1)
- hypocoercivity (1)
- idealclass group (1)
- image analysis (1)
- image denoising (1)
- impulse control (1)
- impurity functions (1)
- incompressible elasticity (1)
- infinite-dimensional analysis (1)
- infinite-dimensional manifold (1)
- inflation-linked product (1)
- integer programming (1)
- integral constitutive equations (1)
- intensity (1)
- inverse optimization (1)
- inverse problem (1)
- isogeometric analysis (IGA) (1)
- jump-diffusion process (1)
- kernel (1)
- kinetic equations (1)
- large investor (1)
- large scale integer programming (1)
- lattice Boltzmann (1)
- level K-algebras (1)
- level set method (1)
- life insurance (1)
- limit theorems (1)
- linear code (1)
- linear systems (1)
- local-global conjectures (1)
- localizing basis (1)
- longevity bonds (1)
- loss analysis (1)
- low-rank approximation (1)
- machine learning (1)
- macro derivative (1)
- market crash (1)
- market manipulation (1)
- markov model (1)
- martingale optimality principle (1)
- mathematical modelling (1)
- mathematical morphology (1)
- matrix problems (1)
- matroid flows (1)
- mean-variance approach (1)
- mesh deformation (1)
- micromechanics (1)
- minimal polynomial (1)
- mixed convection (1)
- mixed methods (1)
- mixed multiscale finite element methods (1)
- modal derivatives (1)
- model order reduction (1)
- moduli space (1)
- monotone Konvergenz (1)
- monotropic programming (1)
- multi scale (1)
- multi-asset option (1)
- multi-class image segmentation (1)
- multi-level Monte Carlo (1)
- multi-phase flow (1)
- multi-scale model (1)
- multicategory (1)
- multifilament superconductor (1)
- multigrid method (1)
- multileaf collimator (1)
- multiobjective optimization (1)
- multipatch (1)
- multiplicative noise (1)
- multiscale denoising (1)
- multiscale methods (1)
- multivariate chi-square-test (1)
- naive diversification (1)
- network flows (1)
- network synthesis (1)
- netzgenerierung (1)
- nicht-newtonsche Strömungen (1)
- nichtlineare Druckkorrektor (1)
- nichtlineare Modellreduktion (1)
- nichtlineare Netzwerke (1)
- non square linear system solving (1)
- non-desarguesian plane (1)
- non-newtonian flow (1)
- nonconvex optimization (1)
- nonlinear circuits (1)
- nonlinear diffusion filtering (1)
- nonlinear elasticity (1)
- nonlinear model reduction (1)
- nonlinear pressure correction (1)
- nonlinear term structure dependence (1)
- nonlinear vibration analysis (1)
- nonlocal filtering (1)
- nonnegative matrix factorization (1)
- nonwovens (1)
- normalization (1)
- number fields (1)
- numerical irreducible decomposition (1)
- numerical methods (1)
- numerics (1)
- numerische Strömungssimulation (1)
- numerisches Verfahren (1)
- oblique derivative (1)
- optimal capital structure (1)
- optimal consumption and investment (1)
- optiman stopping (1)
- option pricing (1)
- option valuation (1)
- partial differential equation (1)
- partial information (1)
- path-dependent options (1)
- pattern (1)
- penalty methods (1)
- penalty-free formulation (1)
- petroleum exploration (1)
- planar polynomial (1)
- poroelasticity (1)
- porous media (1)
- portfolio (1)
- portfolio decision (1)
- portfolio-optimization (1)
- poröse Medien (1)
- posterior collapse (1)
- potential (1)
- preconditioners (1)
- pressure correction (1)
- primal-dual algorithm (1)
- probability distribution (1)
- projective surfaces (1)
- proximation (1)
- proxy modeling (1)
- quadrinomial tree (1)
- quasi-Monte Carlo (1)
- quasi-variational inequalities (1)
- quasihomogeneity (1)
- quasiregular group (1)
- quasireguläre Gruppe (1)
- radiation therapy (1)
- radiotherapy (1)
- rare disasters (1)
- rate of convergence (1)
- raum-zeitliche Analyse (1)
- real quadratic number fields (1)
- reconstructions (1)
- redundant constraint (1)
- reflectionless boundary condition (1)
- reflexionslose Randbedingung (1)
- regime-shift model (1)
- regularization methods (1)
- rheology (1)
- risk analysis (1)
- risk measures (1)
- risk reduction (1)
- sampling (1)
- sawtooth effect (1)
- scalar and vectorial wavelets (1)
- scaled boundary isogeometric analysis (1)
- scaled boundary parametrizations (1)
- second class group (1)
- seismic tomography (1)
- semigroup of values (1)
- semisprays (1)
- sheaf theory (1)
- similarity measures (1)
- singularities (1)
- sparse interpolation of multivariate rational functions (1)
- sparse multivariate polynomial interpolation (1)
- sparsity (1)
- spherical approximation (1)
- sputtering process (1)
- star-shaped domain (1)
- stochastic arbitrage (1)
- stochastic coefficient (1)
- stochastic optimal control (1)
- stochastic processes (1)
- stochastische Arbitrage (1)
- stop- and play-operator (1)
- stratifolds (1)
- subgradient (1)
- superposed fluids (1)
- surface measures (1)
- surrender options (1)
- surrogate algorithm (1)
- syzygies (1)
- tail dependence coefficient (1)
- tax (1)
- tensions (1)
- time delays (1)
- topological asymptotic expansion (1)
- toric geometry (1)
- torische Geometrie (1)
- total variation (1)
- total variation spatial regularization (1)
- translation invariant spaces (1)
- translinear circuits (1)
- translineare Schaltungen (1)
- transmission conditions (1)
- tropical geometry (1)
- unbeschränktes Potential (1)
- unbounded potential (1)
- unimodular certification (1)
- unimodularity (1)
- value semigroup (1)
- valuing contracts (1)
- variable selection (1)
- variational methods (1)
- variational model (1)
- vector bundles (1)
- vector spherical harmonics (1)
- vectorial wavelets (1)
- vertical velocity (1)
- vertikale Geschwindigkeiten (1)
- viscoelastic fluids (1)
- volatility arbitrage (1)
- vortex seperation (1)
- well-posedness (1)
- worst-case (1)
- worst-case scenario (1)
- Äquisingularität (1)
- Überflutung (1)
- Überflutungsrisiko (1)
- Übergangsbedingungen (1)
Faculty / Organisational entity
The thesis is concerned with multiscale approximation by means of radial basis functions on hierarchically structured spherical grids. A new approach is proposed to construct a biorthogonal system of locally supported zonal functions. By use of this biorthogonal system of locally supported zonal functions, a spherical fast wavelet transform (SFWT) is established. Finally, based on the wavelet analysis, geophysically and geodetically relevant problems involving rotation-invariant pseudodifferential operators are shown to be efficiently and economically solvable.
In this thesis, we have dealt with two modeling approaches of the credit risk, namely the structural (firm value) and the reduced form. In the former one, the firm value is modeled by a stochastic process and the first hitting time of this stochastic process to a given boundary defines the default time of the firm. In the existing literature, the stochastic process, triggering the firm value, has been generally chosen as a diffusion process. Therefore, on one hand it is possible to obtain closed form solutions for the pricing problems of credit derivatives and on the other hand the optimal capital structure of a firm can be analysed by obtaining closed form solutions of firm's corporate securities such as; equity value, debt value and total firm value, see Leland(1994). We have extended this approach by modeling the firm value as a jump-diffusion process. The choice of the jump-diffusion process was a crucial step to obtain closed form solutions for corporate securities. As a result, we have chosen a jump-diffusion process with double exponentially distributed jump heights, which enabled us to analyse the effects of jump on the optimal capital structure of a firm. In the second part of the thesis, by following the reduced form models, we have assumed that the default is triggered by the first jump of a Cox process. Further, by following Schönbucher(2005), we have modeled the forward default intensity of a firm as a geometric Brownian motion and derived pricing formulas for credit default swap options in a more general setup than the ones in Schönbucher(2005).
The fast development of the financial markets in the last decade has lead to the creation of a variety of innovative interest rate related products that require advanced numerical pricing methods. Examples in this respect are products with a complicated strong path-dependence such as a Target Redemption Note, a Ratchet Cap, a Ladder Swap and others. On the other side, the usage of the standard in the literature one-factor Hull and White (1990) type of short rate models allows only for a perfect correlation between all continuously compounded spot rates or Libor rates and thus are not suited for pricing innovative products depending on several Libor rates such as for example a "steepener" option. One possible solution to this problem deliver the two-factor short rate models and in this thesis we consider a two-factor Hull and White (1990) type of a short rate process derived from the Heath, Jarrow, Morton (1992) framework by limiting the volatility structure of the forward rate process to a deterministic one. In this thesis, we often choose to use a variety of modified (binomial, trinomial and quadrinomial) tree constructions as a main numerical pricing tool due to their flexibility and fast convergence and (when there is no closed-form solution) compare their results with fine grid Monte Carlo simulations. For the purpose of pricing the already mentioned innovative short-rate related products, in this thesis we offer and examine two different lattice construction methods for the two-factor Hull-White type of a short rate process which are able to deal easily both with modeling of the mean-reversion of the underlying process and with the strong path-dependence of the priced options. Additionally, we prove that the so-called rotated lattice construction method overcomes the typical for the existing two-factor tree constructions problem with obtaining negative "risk-neutral probabilities". With a variety of numerical examples, we show that this leads to a stability in the results especially in cases of high volatility parameters and negative correlation between the base factors (which is typically the case in reality). Further, noticing that Chan et al (1992) and Ritchken and Sankarasubramanian (1995) showed that option prices are sensitive to the level of the short rate volatility, we examine the pricing of European and American options where the short rate process has a volatility structure of a Cheyette (1994) type. In this relation, we examine the application of the two offered lattice construction methods and compare their results with the Monte Carlo simulation ones for a variety of examples. Additionally, for the pricing of American options with the Monte Carlo method we expand and implement the simulation algorithm of Longstaff and Schwartz (2000). With a variety of numerical examples we compare again the stability and the convergence of the different lattice construction methods. Dealing with the problems of pricing strongly path-dependent options, we come across the cumulative Parisian barrier option pricing problem. We notice that in their classical form, the cumulative Parisian barrier options have been priced both analytically (in a quasi closed form) and with a tree approximation (based on the Forward Shooting Grid algorithm, see e.g. Hull and White (1993), Kwok and Lau (2001) and others). However, we offer an additional tree construction method which can be seen as a direct binomial tree integration that uses the analytically calculated conditional survival probabilities. The advantage of the offered method is on one side that the conditional survival probabilities are easier to calculate than the closed-form solution itself and on the other side that this tree construction is very flexible in the sense that it allows easy incorporation of additional features such as e.g a forward starting one. The obtained results are better than the Forward Shooting Grid tree ones and are very close to the analytical quasi closed form solution. Finally, we pay our attention to pricing another type of innovative interest rate alike products - namely the Longevity bond - whose coupon payments depend on the survival function of a given cohort. Due to the lack of a market for mortality, for the pricing of the Longevity bonds we develop (following Korn, Natcheva and Zipperer (2006)) a framework that contains principles from both Insurance and Financial mathematic. Further on, we calibrate the existing models for the stochastic mortality dynamics to historical German data and additionally offer new stochastic extensions of the classical (deterministic) models of mortality such as the Gompertz and the Makeham one. Finally, we compare and analyze the results of the application of all considered models to the pricing of a Longevity bond on the longevity of the German males.
The topic of this thesis is the coupling of an atomistic and a coarse scale region in molecular dynamics simulations with the focus on the reflection of waves at the interface between the two scales and the velocity of waves in the coarse scale region for a non-equilibrium process. First, two models from the literature for such a coupling, the concurrent coupling of length scales and the bridging scales method are investigated for a one dimensional system with harmonic interaction. It turns out that the concurrent coupling of length scales method leads to the reflection of fine scale waves at the interface, while the bridging scales method gives an approximated system that is not energy conserving. The velocity of waves in the coarse scale region is in both models not correct. To circumvent this problems, we present a coupling based on the displacement splitting of the bridging scales method together with choosing appropriate variables in orthogonal subspaces. This coupling allows the derivation of evolution equations of fine and coarse scale degrees of freedom together with a reflectionless boundary condition at the interface directly from the Lagrangian of the system. This leads to an energy conserving approximated system with a clear separation between modeling errors an errors due to the numerical solution. Possible approximations in the Lagrangian and the numerical computation of the memory integral and other numerical errors are discussed. We further present a method to choose the interpolation from coarse to atomistic scale in such a way, that the fine scale degrees of freedom in the coarse scale region can be neglected. The interpolation weights are computed by comparing the dispersion relations of the coarse scale equations and the fully atomistic system. With this new interpolation weights, the number of degrees of freedom can be drastically reduced without creating an error in the velocity of the waves in the coarse scale region. We give an alternative derivation of the new coupling with the Mori-Zwanzig projection operator formalism, and explain how the method can be extended to non-zero temperature simulations. For the comparison of the results of the approximated with the fully atomistic system, we use a local stress tensor and the energy in the atomistic region. Examples for the numerical solution of the approximated system for harmonic potentials are given in one and two dimensions.
Die Arbeit beschäftigt sich mit den Charakteren des Normalisators und des Zentralisators eines Sylowtorus. Dabei wird jede Gruppe G vom Lie-Typ als Fixpunktgruppe einer einfach-zusammenhängenden einfachen Gruppe unter einer Frobeniusabbildung aufgefaßt. Für jeden Sylowtorus S der algebraischen Gruppe wird gezeigt, dass die irreduziblen Charaktere des Zentralisators von S in G sich auf ihre Trägheitsgruppe im Normalisator von S fortsetzen. Diese Fragestellung entsteht aus dem Studium der Höhe 0 Charaktere bei endlichen reduktiven Gruppen vom Lie-Typ im Zusammenhang mit der McKay-Vermutung. Neuere Resultate von Isaacs, Malle und Navarro führen diese Vermutung auf eine Eigenschaft von einfachen Gruppen zurück, die sie dann für eine Primzahl gut nennen. Bei Gruppen vom Lie-Typ zeigt das obige Resultat zusammen mit einer aktuellen Arbeit von Malle einige dabei wichtige und notwendige Eigenschaften. Anhand der Steinberg-Präsentation werden vor allem bei den klassischen Gruppen genauere Aussagen über die Struktur des Zentralisators und des Normalisators eines Sylowtorus bewiesen. Wichtig dabei ist die von Tits eingeführte erweiterte Weylgruppe, die starke Verbindungen zu Zopfgruppen besitzt. Das Resultat wird in zahlreichen Einzelfallbetrachtungen gezeigt, bei denen in dieser Arbeit bewiesene Vererbungsregeln von Fortsetzbarkeitseigenschaften benutzt werden.
This thesis introduces so-called cone scalarising functions. They are by construction compatible with a partial order for the outcome space given by a cone. The quality of the parametrisations of the efficient set given by the cone scalarising functions are then investigated. Here, the focus lies on the (weak) efficiency of the generated solutions, the reachability of effiecient points and continuity of the solution set. Based on cone scalarising functions Pareto Navigation a novel, interactive, multiobjective optimisation method is proposed. It changes the ordering cone to realise bounds on partial tradeoffs. Besides, its use of an equality constraint for the changing component of the reference point is a new feature. The efficiency of its solutions, the reachability of efficient solutions and continuity is then analysed. Potential problems are demonstrated using a critical example. Furthermore, the use of Pareto Navigation in a two-phase approach and for nonconvex problems is discussed. Finally, its application for intensity-modulated radiotherapy planning is described. Thereby, its realisation in a graphical user interface is shown.
This thesis deals with modeling aspects of generalized Newtonian and of non-Newtonian fluids, as well as with development and validation of algorithms used in simulation of such fluids. The main contribution in the modeling part are the introduction and analysis of a new model for the generalized Newtonian fluids, where constitutive equation is of an algebraic form. Distinction between shear and extensional viscosities leads to anisotropic viscosity model. It can be considered as a natural extension of the well known (isotropic viscosity) Carreau model, which deals only with shear viscosity properties of the fluid. The proposed model takes additionally into account extensional viscosity properties. Numerical results show that the anisotropic viscosity model gives much better agreement with experimental observations than the isotropic one. Another contribution of the thesis consists of the development and analysis of robust and reliable algorithms for simulation of generalized Newtonian fluids. For such fluids the momentum equations are strongly coupled through mixed derivatives appearing in the viscous term (unlike the case of Newtonian fluids). It is shown in this thesis, that a careful treatment of those derivatives is essential in deriving robust algorithms. A modification of a standard SIMPLE-like algorithm is given, where all the viscous terms from the momentum equations are discretized in an implicit manner. Moreover, it is shown that a block diagonal preconditioner to the viscous operator is good enough to be used in simulations. Furthermore, different solution techniques, namely projection type methods (consists of solving momentum equations and pressure correction equation) and fully coupled methods (momentum and continuity equations are solved together), are compared. It is shown, that explicit discretization of the mixed derivatives lead to stability problems. Further, analytical estimates of eigenvalue distribution for three different preconditioners, applied to the transformed system arising after discretization and linearization of the momentum and continuity equations, are provided. We propose to apply a block Gauss-Seidel preconditioner to the transformed system. The analysis shows, that this preconditioner is able to cluster eigenvalues around unity independent of the transformation step. It is not the case for other preconditioners applied to the transformed system as discussed in the thesis. The block Gauss-Seidel preconditioner has also shown the best behavior (among all preconditioners discussed in the thesis) in numerical experiments. Further contribution consists of comparison and validation of numerical algorithms applied in simulations of non-Newtonian fluids modeled by time integral constitutive equations. Numerical results from simulations of dilute polymer solutions, described by the integral Oldroyd B model, have shown very good quantitative agreement with the results obtained by differential Oldroyd B counterpart in 4:1 planar contraction domain at low Weissenberg numbers. In this case, the Weissenberg number is changed by changing the relaxation time. However, contrary to the differential Oldroyd B model, the integral one allows to perform stable simulations also in the range of high Weissenberg numbers. Moreover, very good agreement with experimental observations has been achieved. Simulations of concentrated polymer solutions (polystyrene and polybutadiene solutions), modeled by the integral Doi Edwards model, supplemented by chain length fluctuations, have shown very good qualitative agreement with the results obtained by its differential approximation in 4:1:4 constriction domain. Again, much higher Weissenberg numbers can be achieved when the integral model is used. Moreover, very good quantitative results with experimental data of polystyrene solution for the first normal stress difference and shear viscosity defined here as the quotient of a shear stress and a shear rate. Finally, comparison of the two methods used for approximating the time integral constitutive equation, namely Deformation Field Method (DFM) and Backward Lagrangian Particle Method (BLPM), is performed. In BLPM the particle paths are recalculated at every time step of the simulations, what has never been tried before. The results have shown, that in the considered geometries both methods give similar results.
This work deals with the mathematical modeling and numerical simulation of the dynamics of a curved inertial viscous Newtonian fiber, which is practically applicable to the description of centrifugal spinning processes of glass wool. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a three-dimensional free boundary value problem via instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the fiber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional fiber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms. For the numerical simulation of the derived model a finite volume code is developed. The results of the numerical scheme for high Reynolds numbers are validated by comparing them with the analytical solution of the inviscid problem. Moreover, the influence of parameters, like viscosity and rotation on the fiber dynamics are investigated. Finally, an application based on industrial data is performed.
The new international capital standard for credit institutions (“Basel II”) allows banks to use internal rating systems in order to determine the risk weights that are relevant for the calculation of capital charge. Therefore, it is necessary to develop a system that enfolds the main practices and methods existing in the context of credit rating. The aim of this thesis is to give a suggestion of setting up a credit rating system, where the main techniques used in practice are analyzed, presenting some alternatives and considering the problems that can arise from a statistical point of view. Finally, we will set up some guidelines on how to accomplish the challenge of credit scoring. The judgement of the quality of a credit with respect to the probability of default is called credit rating. A method based on a multi-dimensional criterion seems to be natural, due to the numerous effects that can influence this rating. However, owing to governmental rules, the tendency is that typically one-dimensional criteria will be required in the future as a measure for the credit worthiness or for the quality of a credit. The problem as described above can be resolved via transformation of a multi-dimensional data set into a one-dimensional one while keeping some monotonicity properties and also keeping the loss of information (due to the loss of dimensionality) at a minimum level.
Tropical geometry is a rather new field of algebraic geometry. The main idea is to replace algebraic varieties by certain piece-wise linear objects in R^n, which can be studied with the aid of combinatorics. There is hope that many algebraically difficult operations become easier in the tropical setting, as the structure of the objects seems to be simpler. In particular, tropical geometry shows promise for application in enumerative geometry. Enumerative geometry deals with the counting of geometric objects that are determined by certain incidence conditions. Until around 1990, not many enumerative questions had been answered and there was not much prospect of solving more. But then Kontsevich introduced the moduli space of stable maps which turned out to be a very useful concept for the study of enumerative geometry. A well-known problem of enumerative geometry is to determine the numbers N_cplx(d,g) of complex genus g plane curves of degree d passing through 3d+g-1 points in general position. Mikhalkin has defined the analogous number N_trop(d,g) for tropical curves and shown that these two numbers coincide (Mikhalkin's Correspondence Theorem). Tropical geometry supplies many new ideas and concepts that could be helpful to answer enumerative problems. However, as a rather new field, tropical geometry has to be studied more thoroughly. This thesis is concerned with the ``translation'' of well-known facts of enumerative geometry to tropical geometry. More precisely, the main results of this thesis are: - a tropical proof of the invariance of N_trop(d,g) of the position of the 3d+g-1 points, - a tropical proof for Kontsevich's recursive formula to compute N_trop(d,0) and - a tropical proof of Caporaso's and Harris' algorithm to compute N_trop(d,g). All results were derived in joint work with my advisor Andreas Gathmann. (Note that tropical research is not restricted to the translation of classically well-known facts, there are actually new results shown by means of tropical geometry that have not been known before. For example, Mikhalkin gave a tropical algorithm to compute the Welschinger invariant for real curves. This shows that tropical geometry can indeed be a tool for a better understanding of classical geometry.)