Weak existence and uniqueness for affine stochastic Volterra equations with \(L^1\)-kernels

DOI10.3150/20-BEJ1284zbMath1480.60142arXiv1912.07445MaRDI QIDQ2040079

Eduardo Abi Jaber

Publication date: 9 July 2021

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.07445

zbMATH Keywords

Hawkes processesstochastic Volterra equationssuperprocessesrough volatilityaffine Volterra processesRiccati-Volterra equations

Mathematics Subject Classification ID

Stochastic integrals (60H05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (12)

Utility Maximization in Multivariate Volterra Models ⋮ On the Discrete-Time Simulation of the Rough Heston Model ⋮ The characteristic function of Gaussian stochastic volatility models: an analytic expression ⋮ Approximation of Stochastic Volterra Equations with kernels of completely monotone type ⋮ One-dimensional McKean-Vlasov stochastic Volterra equations with Hölder diffusion coefficients ⋮ Stochastic Volterra equations with Hölder diffusion coefficients ⋮ VIX pricing in the rBergomi model under a regime switching change of measure ⋮ On the existence of weak solutions to stochastic Volterra equations ⋮ Affine Volterra processes with jumps ⋮ Log-Modulated Rough Stochastic Volatility Models ⋮ A weak solution theory for stochastic Volterra equations of convolution type ⋮ Existence and uniqueness of solutions for the stochastic Volterra-Levin equation with variable delays

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functional analysis, Sobolev spaces and partial differential equations
• Critical branching in a highly fluctuating random medium
• A super-Brownian motion with a single point catalyst
• Continuous-time asset pricing theory. A martingale-based approach
• A new approach to the single point catalytic super-Brownian motion
• Singularity of super-Brownian local time at a point catalyst
• Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case
• Affine Volterra processes
• Markovian structure of the Volterra Heston model
• Space-time regularity of catalytic super-Brownian motion
• The stochastic Fubini theorem revisited
• A cluster process representation of a self-exciting process
• [https://portal.mardi4nfdi.de/wiki/Publication:4155579 Sur l'int�grabilit� uniforme des martingales exponentielles]
• Volatility is rough
• Lifting the Heston model
• Multifactor Approximation of Rough Volatility Models
• Fractional Brownian Motions, Fractional Noises and Applications
• The characteristic function of rough Heston models
• No‐arbitrage implies power‐law market impact and rough volatility

This page was built for publication: Weak existence and uniqueness for affine stochastic Volterra equations with \(L^1\)-kernels