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We investigate rough differential equations with a time-dependent reflecting lower barrier, where both the driving (rough) path and the barrier itself may have jumps. Assuming the driving signals allow for Young integration, we provide existence, uniqueness and stability results. When the driving signal is a c`adl`ag $p$-rough path for $p in [2,3)$, we establish existence to general reflected rough differential equations, as well as uniqueness in the one-dimensional case.
Using rough path theory, we provide a pathwise foundation for stochastic It^o integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, w
In this note we consider differential equations driven by a signal $x$ which is $gamma$-Holder with $gamma>1/3$, and is assumed to possess a lift as a rough path. Our main point is to obtain existence of solutions when the coefficients of the equatio
We develop the rough path counterpart of It^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It^o / forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed.
To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting SDEs (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting SDEs with s
In this paper we solve real-valued rough differential equations (RDEs) reflected on an irregular boundary. The solution $Y$ is constructed as the limit of a sequence $(Y^n)_{ninmathbb{N}}$ of solutions to RDEs with unbounded drifts $(psi_n)_{ninmathb