Affine Volterra processes

@article{Jaber2019AffineVP,
  title={Affine Volterra processes},
  author={Eduardo Abi Jaber and Martin Larsson and Sergio Pulido},
  journal={The Annals of Applied Probability},
  year={2019}
}
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 semimartingales, nor Markov processes in general. We provide explicit exponential-affine representations of the Fourier-Laplace functional in terms of the solution of an associated system of deterministic integral equations of convolution type, extending well-known… 

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References

SHOWING 1-10 OF 31 REFERENCES

The affine transform formula for affine jump-diffusions with a general closed convex state space

We establish existence of exponential moments and the validity of the affine transform formula for affine jump-diffusions with a general closed convex state space. This extends known results for

Corrections to: Extending the martingale measure stochastic integral with applications to spatially homogeneous S.P.D.E. 's

We extend the definition of Walsh's martingale measure stochastic integral so as to be able to solve stochastic partial differential equations whose Green's function is not a function but a Schwartz

Affine processes with compact state space

The behavior of affine processes, which are ubiquitous in a wide range of applications, depends crucially on the choice of state space. We study the case where the state space is compact, and prove

Sample Path Properties of Volterra Processes

We consider the regularity of sample paths of Volterra processes. These processes are defined as stochastic integrals $$ M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}_{+}, $$ where $X$ is a

The characteristic function of rough Heston models

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to

Regularity Properties of Some Stochastic Volterra Integrals with Singular Kernel

We prove the Hölder continuity of some stochastic Volterra integrals, with singular kernels, under integrability assumptions on the integrand. Some applications to processes arising in the analysis

Affine Diffusions with Non-Canonical State Space

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

Uniqueness for Volterra-type stochastic integral equations

We study uniqueness for a class of Volterra-type stochastic integral equations. We focus on the case of non-Lipschitz noise coefficients. The connection of these equations to certain degenerate

Continuous martingales and Brownian motion

0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.-