8 papers · 1 filter
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…
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…
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…
Robust Filtering and Propagation of Uncertainty in Hidden Markov Models
Andrew L. Allan
We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no pr…
Pathwise Stochastic Control with Applications to Robust Filtering
Andrew L. Allan, Samuel N. Cohen
We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms o…
Parameter Uncertainty in the Kalman-Bucy Filter
Andrew L. Allan, Samuel N. Cohen
In standard treatments of stochastic filtering one first has to estimate the values of the parameters of the model. Simply running the filter without considering the reliability of…
Ergodic Backward Stochastic Difference Equations
Andrew L. Allan, Samuel N. Cohen
We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness…