8 papers
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…
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…
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…
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…