The rough Hawkes Heston stochastic volatility model
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 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 …
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
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 …
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 …
(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 …
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 …
for short) with completely monotone kernels and non-degenerate noise under mild regularity …
Affine Volterra processes with jumps
The theory of affine processes has been recently extended to continuous stochastic Volterra
equations. These so-called affine Volterra processes overcome modeling shortcomings of …
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 …
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 …
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 …
the convex order on the space of continuous\({\mathbb {R}}^{d}\)-valued paths and for the …