The rough Hawkes Heston stochastic volatility model

A Bondi, S Pulido, S Scotti - Mathematical Finance, 2024 - Wiley Online Library
We study an extension of the Heston stochastic volatility model that incorporates rough
volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston …

Volatility models in practice: Rough, Path-dependent or Markovian?

E Abi Jaber, SX Li - Path-Dependent or Markovian, 2024 - papers.ssrn.com
Volatility models in practice: Rough, Path-dependent or Markovian? Page 1 Volatility
models in practice: Rough, Path-dependent or Markovian? Eduardo Abi Jaber *1 and …

Designing universal causal deep learning models: The case of infinite-dimensional dynamical systems from stochastic analysis

L Galimberti, A Kratsios, G Livieri - arXiv preprint arXiv:2210.13300, 2022 - arxiv.org
Causal operators (CO), such as various solution operators to stochastic differential
equations, play a central role in contemporary stochastic analysis; however, there is still no …

Markovian lifting and asymptotic log-Harnack inequality for stochastic Volterra integral equations

Y Hamaguchi - Stochastic Processes and their Applications, 2024 - Elsevier
We introduce a new framework of Markovian lifts of stochastic Volterra integral equations
(SVIEs for short) with completely monotone kernels. We define the state space of the …

Weak existence and uniqueness for affine stochastic Volterra equations with -kernels

E Abi Jaber - 2021 - projecteuclid.org
We provide existence, uniqueness and stability results for affine stochastic Volterra
equations with L 1-kernels and jumps. Such equations arise as scaling limits of branching …

Weak well-posedness of stochastic Volterra equations with completely monotone kernels and non-degenerate noise

Y Hamaguchi - arXiv preprint arXiv:2310.16030, 2023 - arxiv.org
We establish weak existence and uniqueness in law for stochastic Volterra equations (SVEs
for short) with completely monotone kernels and non-degenerate noise under mild regularity …

Affine Volterra processes with jumps

A Bondi, G Livieri, S Pulido - Stochastic Processes and their Applications, 2024 - Elsevier
The theory of affine processes has been recently extended to continuous stochastic Volterra
equations. These so-called affine Volterra processes overcome modeling shortcomings of …

Stochastic Volterra equations with Hölder diffusion coefficients

DJ Prömel, D Scheffels - Stochastic Processes and their Applications, 2023 - Elsevier
The existence of strong solutions and pathwise uniqueness are established for one-
dimensional stochastic Volterra equations with locally Hölder continuous diffusion …

On the discrete-time simulation of the rough Heston model

A Richard, X Tan, F Yang - SIAM Journal on Financial Mathematics, 2023 - SIAM
We study Euler-type discrete-time schemes for the rough Heston model, which can be
described by a stochastic Volterra equation (with non-Lipschitz coefficient functions) or by an …

Convex ordering for stochastic Volterra equations and their Euler schemes

B Jourdain - Finance and Stochastics, 2024 - Springer
In this paper, we are interested in comparing solutions to stochastic Volterra equations for
the convex order on the space of continuous\({\mathbb {R}}^{d}\)-valued paths and for the …