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Tractable multi-firm default models based on discontinuous processes
The aim of this thesis is to thoroughly study structural default models based on jump-diffusion processes. Jump-diffusion models were first proposed by Zhou (2001), who also showed that these models have several desirable ...
Über globale und lokale Einbettungen
Let X : Omega -> R³ element of C^1(Omega) be a vector valued mapping defined on the domain Omega C R². In this thesis we study the system of differential equations (dX)² = ds² where the right handed side ds² = gij dx^i ...
Exchangeability of copulas
(Universität Ulm, 2016-07-08)
When studying the dependence structure of multivariate random vectors, the copula is crucial. A copula is called exchangeable, if it is invariant under any permutation of its arguments. In this thesis, a limit for the ...
Statistical analysis of spatial point patterns - applications to economical, biomedical and ecological data
The aim of this thesis is to investigate, implement and apply different techniques of statistical point pattern analysis. In the last years, several projects at the Institute of Stochastics at Ulm University dealt with ...
On algorithms for coding and decoding algebraic-geometric codes and their implementation
In this thesis algorithms for coding and decoding algebraic-geometric codes are developed and their implementation is discussed. The algorithms for coding include methods to compute Riemann-Roch spaces and algorithms to ...
Zur Automatisierung von Softwaretests - Entwicklung und Bewertung von Orakellösungen
All large software systems contain bugs. Therefore the identification and the removal of these bugs is an important and time consuming task, responsible for a large slice of the software development schedule. The testing ...
Robuste Portfolio Optimierung in Lévy Märkten
Berechnung eines optimalen Konsumprozesses und einer zugehörigen Investmentstrategie mittels der Martingalmethode
Optimal control of Markovian jump processes with different information structures
We consider a stochastic control problem where only groups of states of a Markovian jump process and not the complete state process is observable. In particular the Hidden-Markov-model and the Bayes-model are included. ...
Nichtlineare partielle Differentialgleichungen vom gemischten elliptisch-hyperbolischen Typ
(Universität Ulm, 2017-08-28)
This thesis studies the article "Local solutions to a class of Monge-Ampère equations of mixed type" by Qing Han (Duke Math. J., Vol. 136, No. 3, 2007). The article proves the existence of sufficiently smooth local solutions ...
Credit portfolio modelling with elliptically contoured distributions - approximation, pricing, dynamisation
The aim of this thesis is to introduce a new set of factor models for the pricing of portfolio credit derivatives, which match the observations on the derivatives markets better than the standard Gaussian model. These new ...