32 citations · 67 across the 24 of their papers we have counts for
30 papers
Approximate Transitivity of Young Translation on Rough Paths
Carlo Bellingeri, Paul Gassiat, Hugo Nouaille
We show that Young translation has dense orbits in the space of rough paths: for any two geometric rough paths, one can translate the first by a sequence of smooth paths so that it…
Martingale property and moment explosions in signature volatility models
Eduardo Abi Jaber, Paul Gassiat, Dimitri Sotnikov
We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of…
A gradient flow on control space with rough initial condition
Paul Gassiat, Florin Suciu
We consider the (sub-Riemannian type) control problem of finding a path going from an initial point to a target point , by only moving in certain admissible directions. We a…
Zero noise limit for singular ODE regularized by fractional noise
Łukasz Mądry, Paul Gassiat
We consider scalar ODE with a power singularity at the origin, regularized by an additive fractional noise. We show that, as the intensity in front of the noise goes to , the so…
Gaussian Rough Paths Lifts via Complementary Young Regularity
Paul Gassiat, Tom Klose
Inspired by recent advances in singular SPDE theory, we use the Poincaré inequality on Wiener space to show that controlled complementary Young regularity is sufficient to obtain G…
Long-time behaviour of stochastic Hamilton-Jacobi equations
Paul Gassiat, Benjamin Gess, Pierre-Louis Lions +1
The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpe…
Perturbations of singular fractional SDEs
Paul Gassiat, Łukasz Mądry
We obtain well-posedness results for a class of ODE with a singular drift and additive fractional noise, whose right-hand-side involves some bounded variation terms depending on th…
Weak error rates of numerical schemes for rough volatility
Paul Gassiat
Simulation of rough volatility models involves discretization of stochastic integrals where the integrand is a function of a (correlated) fractional Brownian motion of Hurst index…
The Neumann problem for fully nonlinear SPDE
Paul Gassiat, Benjamin Seeger
We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set o…
Short dated smile under Rough Volatility: asymptotics and numerics
Peter K. Friz, Paul Gassiat, Paolo Pigato
In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2021] we introduce a new methodology to analyze large classes of (classical and rough) stochasti…
Non-uniqueness for reflected rough differential equations
Paul Gassiat
We give an example of a reflected diffferential equation which may have infinitely many solutions if the driving signal is rough enough (e.g. of infinite -variation, for some $p…
A Free Boundary Characterisation of the Root Barrier for Markov Processes
Paul Gassiat, Harald Oberhauser, Christina Z. Zou
We study the existence, optimality, and construction of non-randomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality…
On the martingale property in the rough Bergomi model
Paul Gassiat
We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussia…
Precise asymptotics: robust stochastic volatility models
Peter K. Friz, Paul Gassiat, Paolo Pigato
We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option p…
Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
Paul Gassiat, Benjamin Gess, Pierre-Louis Lions +1
We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed…
Existence of densities for the dynamic model
Paul Gassiat, Cyril Labbé
We apply Malliavin calculus to the equation on the torus and prove existence of densities for the solution of the equation evaluated at regular enough test functions. We wo…
A regularity structure for rough volatility
Christian Bayer, Peter K. Friz, Paul Gassiat +2
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market…
A stochastic Hamilton-Jacobi equation with infinite speed of propagation
Paul Gassiat
We give an example of a stochastic Hamilton-Jacobi equation which has an infinite speed of propagation as soon as the driving signal is not of bounded variation…
Regularization by noise for stochastic Hamilton-Jacobi equations
Paul Gassiat, Benjamin Gess
We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path bounds for the second derivative of solutions…
Eikonal equations and pathwise solutions to fully non-linear SPDEs
Peter K. Friz, Paul Gassiat, Pierre-Louis Lions +1
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associa…
Malliavin Calculus for regularity structures: the case of gPAM
Giuseppe Cannizzaro, Peter K. Friz, Paul Gassiat
Malliavin calculus is implemented in the context of [M. Hairer, A theory of regularity structures, Invent. Math. 2014]. This involves some constructions of independent interest, no…
An integral equation for Root's barrier and the generation of Brownian increments
Paul Gassiat, Aleksandar Mijatović, Harald Oberhauser
We derive a nonlinear integral equation to calculate Root's solution of the Skorokhod embedding problem for atom-free target measures. We then use this to efficiently generate boun…
Stochastic control with rough paths
Joscha Diehl, Peter Friz, Paul Gassiat
We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum p…
Root's barrier, viscosity solutions of obstacle problems and reflected FBSDEs
Paul Gassiat, Harald Oberhauser, Goncalo dos Reis
We revisit work of Rost, Dupire and Cox--Wang on connections between Root's solution of the Skorokhod embedding problem and obstacle problems. We develop an approach based on visco…