Related papers: Affine realizations with affine state processes fo…
The goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by L\'evy processes admits an affine realization. Our results are accompanied by several examples arising in natural sciences and…
In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite…
This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for…
We propose an alternative approach on the existence of affine realizations for HJM interest rate models. It is applicable to a wide class of models, and simultaneously it is conceptually rather comprehensible. We also supplement some known…
This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine…
Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and…
We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions…
Multivariate process satisfying affine stochastic recurrence equation with generic diagonal matrices is considered. We prove that the stationary solution is regularly varying. The results are applicable to diagonal autoregressive models.
The goal of this paper is to clarify when the solutions to stochastic partial differential equations stay close to a given subset of the state space for starting points which are close as well. This includes results for deterministic…
We show that stochastically continuous, time-homogeneous affine processes on the canonical state space $\Rplus^m \times \RR^n$ are always regular. In the paper of \citet{Duffie2003} regularity was used as a crucial basic assumption. It was…
We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of an affine process, namely as…
This paper studies the large fluctuations of solutions of finite--dimensional affine stochastic neutral functional differential equations with finite memory, as well as related nonlinear equations. We find conditions under which the exact…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we…
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined…
We put forward a complete theory on moment explosion for fairly general state-spaces. This includes a characterization of the validity of the affine transform formula in terms of minimal solutions of a system of generalized Riccati…
A stochastic affine evolution equation with bilinear noise term is studied where the driving process is a real-valued fractional Brownian motion. Stochastic integration is understood in the Skorokhod sense. Existence and uniqueness of weak…
This work is devoted to the study of conservative affine processes on the canonical state space $D = $R_+^m \times \R^n$, where $m + n > 0$. We show that each affine process can be obtained as the pathwise unique strong solution to a…