Related papers: Affine Processes
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…
We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…
We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither…
We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in…
We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterized by the affine form of their cumulant…
We consider local martingales which are standard or stochastic exponentials M of one component X of a multivariate affine process in the sense of Duffie, Filipovic and Schachermayer (2003). By completing their characterization of…
We present a time change construction of affine processes with state-space $\mathbb{R}_+^m\times \mathbb{R}^n$. These processes were systematically studied in (Duffie, Filipovi\'c and Schachermayer, 2003) since they contain interesting…
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…
We study the long-time behavior of affine processes on positive self-adjoiont Hilbert-Schmidt operators which are of pure-jump type, conservative and have finite second moment. For subcritical processes we prove the existence of a unique…
We consider stochastic (partial) differential equations appearing as Markovian lifts of affine Volterra processes with jumps from the point of view of the generalized Feller property which was introduced in e.g.~\cite{doetei:10}. In…
First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space $R_+ \times R^d$. We specialize our result to one-dimensional continuous state branching processes with immigration.…
We introduce a class of measure-valued processes, which -- in analogy to their finite dimensional counterparts -- will be called measure-valued polynomial diffusions. We show the so-called moment formula, i.e.~a representation of the…
Discrete-time affine processes are widely used in finance and economics and encompass count, positive, and nonnegative-valued processes. This paper develops near-unit-root asymptotic theory for this class of models. Unlike linear AR(1)…
In this paper, sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space $\mathbb{R}_{\geqslant0}^{m}\times\mathbb{R}^{n}$, where $m,\thinspace…
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…
We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result…
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…
We introduce a flexible and tractable infinite-dimensional stochastic volatility model. More specifically, we consider a Hilbert space valued Ornstein-Uhlenbeck-type process, whose instantaneous covariance is given by a pure-jump stochastic…
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…
Multidimensional affine diffusions have been studied in detail for the case of a canonical state space. We present results for general state spaces and provide a complete characterization of all possible affine diffusions with polyhedral…