Affine Volterra processes with jumps

Bondi, Alessandro, Livieri, Giulia ORCID: 0000-0002-3777-7329 and Pulido, Sergio (2024) Affine Volterra processes with jumps. Stochastic Processes and Their Applications, 168. ISSN 0304-4149

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Abstract

The theory of affine processes has been recently extended to continuous stochastic Volterra equations. These so-called affine Volterra processes overcome modeling shortcomings of affine processes by incorporating path-dependent features and trajectories with regularity different from the paths of Brownian motion. More specifically, singular kernels yield rough affine processes. This paper extends the theory by considering affine stochastic Volterra equations with jumps. This extension is not straightforward because the jump structure and possible singularities of the kernel may induce explosions of the trajectories. This study also provides exponential affine formulas for the conditional Fourier–Laplace transform of marked Hawkes processes.

Item Type:	Article
Official URL:	https://www.sciencedirect.com/journal/stochastic-p...
Additional Information:	© 2023 Elsevier B.V.
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	14 Dec 2023 12:39
Last Modified:	20 Nov 2024 03:51
URI:	http://eprints.lse.ac.uk/id/eprint/121054

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