Outputs (8)

Pathwise Convergence of the Euler Scheme for Rough and Stochastic Differential Equations (2025)
Journal Article
Allan, A., Kwossek, A., Liu, C., & Prömel, D. (in press). Pathwise Convergence of the Euler Scheme for Rough and Stochastic Differential Equations. Journal of the London Mathematical Society,

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 càdlàg paths satisfying a suitable criterion, namely the so-called Property... Read More about Pathwise Convergence of the Euler Scheme for Rough and Stochastic Differential Equations.

A càdlàg rough path foundation for robust finance (2023)
Journal Article
Allan, A. L., Liu, C., & Prömel, D. J. (2024). A càdlàg rough path foundation for robust finance. Finance and Stochastics, 28(1), 215-257. https://doi.org/10.1007/s00780-023-00522-0

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 markets, including those under Knightian uncertainty. To this end, we... Read More about A càdlàg rough path foundation for robust finance.

Model‐free portfolio theory: A rough path approach (2023)
Journal Article
Allan, A. L., Cuchiero, C., Liu, C., & Prömel, D. J. (2023). Model‐free portfolio theory: A rough path approach. Mathematical Finance, 33(3), 709-765. https://doi.org/10.1111/mafi.12376

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 compared to previous model-free approaches based on Föllmer integration. With... Read More about Model‐free portfolio theory: A rough path approach.

Càdlàg rough differential equations with reflecting barriers (2021)
Journal Article
Allan, A. L., Liu, C., & Prömel, D. J. (2021). Càdlàg rough differential equations with reflecting barriers. Stochastic Processes and their Applications, 142, 79-104. https://doi.org/10.1016/j.spa.2021.08.004

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, uni... Read More about Càdlàg rough differential equations with reflecting barriers.

Robust filtering and propagation of uncertainty in hidden Markov models (2021)
Journal Article
Allan, A. L. (2021). Robust filtering and propagation of uncertainty in hidden Markov models. Electronic Journal of Probability, 26, 1-37. https://doi.org/10.1214/21-ejp633

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 prior or stochastic model is available. We quantify and analyze how the... Read More about Robust filtering and propagation of uncertainty in hidden Markov models.

Pathwise stochastic control with applications to robust filtering (2020)
Journal Article
Allan, A. L., & Cohen, S. N. (2020). Pathwise stochastic control with applications to robust filtering. Annals of Applied Probability, 30(5), 2274-2310. https://doi.org/10.1214/19-aap1558

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 of the optimal control of rough differential equations. We investigate... Read More about Pathwise stochastic control with applications to robust filtering.

Parameter Uncertainty in the Kalman--Bucy Filter (2019)
Journal Article
Allan, A. L., & Cohen, S. N. (2019). Parameter Uncertainty in the Kalman--Bucy Filter. SIAM Journal on Control and Optimization, 57(3), 1646-1671. https://doi.org/10.1137/18m1167693

In standard treatments of stochastic filtering one first has to estimate the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional source of statistical unce... Read More about Parameter Uncertainty in the Kalman--Bucy Filter.

Ergodic backward stochastic difference equations (2016)
Journal Article
Allan, A. L., & Cohen, S. N. (2016). Ergodic backward stochastic difference equations. Stochastics: An International Journal of Probability and Stochastic Processes, 88(8), 1207-1239. https://doi.org/10.1080/17442508.2016.1224881

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 of solutions, along with a comparison theorem. To obtain this result,... Read More about Ergodic backward stochastic difference equations.