5 citations · 8 across the 12 of their papers we have counts for
18 papers
The -bounds for Derivatives of Unitary Developments of Random Continuous Geometric Rough Paths
Chong Liu, Zijiu Lyu, Hao Ni
In this paper we derive an explicit formula for derivatives of unitary developments of random continuous geometric rough paths of all orders and establish proper -bounds for t…
Signature inversion of axial linear curves
Chong Liu, Shi Wang
We introduce a signature inversion scheme for -axial linear curves which are widely used in various areas. We show that in the presence of a linear coordinate function, the de…
Pathwise analysis of log-optimal portfolios
Andrew L. Allan, Anna P. Kwossek, Chong Liu +1
Based on the theory of càdlàg rough paths, we develop a pathwise approach to analyze stability and approximation properties of portfolios along individual price trajectories genera…
Pathwise convergence of the Euler scheme for rough and stochastic differential equations
Andrew L. Allan, Anna P. Kwossek, Chong Liu +1
The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by càdlà…
Optimal Stopping via Distribution Regression: a Higher Rank Signature Approach
Blanka Horvath, Maud Lemercier, Chong Liu +2
Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target. The learning procedure based on the notio…
An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning
Anastasis Kratsios, Chong Liu, Matti Lassas +2
Motivated by the developing mathematics of deep learning, we build universal functions approximators of continuous maps between arbitrary Polish metric spaces and $\m…
A Càdlàg Rough Path Foundation for Robust Finance
Andrew L. Allan, Chong Liu, David J. Prömel
Using rough path theory, we provide a pathwise foundation for stochastic Itô integration, which covers most commonly applied trading strategies and mathematical models of financial…
Model-free Portfolio Theory: A Rough Path Approach
Andrew L. Allan, Christa Cuchiero, Chong Liu +1
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compare…
A Sobolev rough path extension theorem via regularity structures
Chong Liu, David J. Prömel, Josef Teichmann
We show that every -valued Sobolev path with regularity and integrability can be lifted to a Sobolev rough path provided . The novelty of our appr…
Càdlàg Rough Differential Equations with Reflecting Barriers
Andrew L. Allan, Chong Liu, David J. Prömel
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…
On Sobolev rough paths
Chong Liu, David J. Prömel, Josef Teichmann
We introduce the space of rough paths with Sobolev regularity and the corresponding concept of controlled Sobolev paths. Based on these notions, we study rough path integration and…
Adapted Topologies and Higher Rank Signatures
Patric Bonnier, Chong Liu, Harald Oberhauser
The topology of weak convergence does not account for the growth of information over time that is captured in the filtration of an adapted stochastic process. For example, two adap…
Supermartingale deflators in the absence of a numéraire
Philipp Harms, Chong Liu, Ariel Neufeld
In this paper we study arbitrage theory of financial markets in the absence of a numéraire both in discrete and continuous time. In our main results, we provide a generalization of…
Optimal extension to Sobolev rough paths
Chong Liu, David J. Prömel, Josef Teichmann
We show that every -valued Sobolev path with regularity and integrability can be lifted to a Sobolev rough path in the sense of T. Lyons provided . M…
Characterization of non-linear Besov spaces
Chong Liu, David J. Prömel, Josef Teichmann
The canonical generalizations of two classical norms on Besov spaces are shown to be equivalent even in the case of non-linear Besov spaces, that is, function spaces consisting of…
Examples of Itô càdlàg rough paths
Chong Liu, David J. Prömel
Based on a dyadic approximation of Itô integrals, we show the existence of Itô càdlàg rough paths above general semimartingales, suitable Gaussian processes and non-negative typica…
Stochastic Analysis with Modelled Distributions
Chong Liu, David J. Prömel, Josef Teichmann
Using a Besov topology on spaces of modelled distributions in the framework of Hairer's regularity structures, we prove the reconstruction theorem on these Besov spaces with negati…
Compactness Criterion for Semimartingale Laws and Semimartingale Optimal Transport
Chong Liu, Ariel Neufeld
We provide a compactness criterion for the set of laws on the Skorokhod space for which the canonical process is a semimartingale having absolutely…