# Registered Data

## [01165] Adapted Wasserstein distance for robust finance

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__D505__**Type**: Proposal of Minisymposium**Abstract**: The minisymposium brings together scientists working on the developments of new transport distances suited for the analysis of financial markets in case of model uncertainty. The four talks illustrate the powerful use of newly developed tools in optimal transport, and in particular of the Adapted Wasserstein distance, to tackle crucial problems in finance, such as robustness of optimal decision making to model misspecification.**Organizer(s)**: Beatrice Acciaio**Sponsor**: This session is sponsored by the SIAM Activity Group on Financial Mathematics and Engineering.**Classification**:__91G80__,__49Q22__**Minisymposium Program**:- 01165 (1/1) :
__5D__@__D505__[Chair: Beatrice Acciaio] **[05605] Adapted Wasserstein distance for model-uncertainty in finance****Format**: Talk at Waseda University**Author(s)**:**Beatrice Acciaio**(ETH ZurichH Zurich)

**Abstract**: I will illustrate the suitability of adapted transport distances in the context of model-uncertainty in finance. I will then present two consistent estimators for the Adapted Wasserstein distance, showing that we can recover the optimal rates of the classical empirical measure with respect to Wasserstein distance.

**[05607] Adapted Wasserstein distance on the space of continuous time stochastic processes.****Format**: Talk at Waseda University**Author(s)**:**Beatrice Acciaio**(ETH Zurich)- Xin Zhang (University of Vienna)

**Abstract**: Stochastic processes are often used as models for stock prices, and people were interested in the stability of optimal stopping problem in Finance with respect to the underlying model. We define the adapted Wasserstein distance on the space of stochastic processes, which is an extension of the usual Wasserstein distance between laws of stochastic processes. We prove that the optimal stopping problem is continuous with respect to the resulting topology, Martingales form a closed subset and approximation results like Donsker's theorem extend to the adapted Wasserstein distance.

**[05608] On concentration of the empirical measure for general transport costs****Format**: Talk at Waseda University**Author(s)**:**Beatrice Acciaio**(ETH Zurich)- Johannes Wiesel (CMU)

**Abstract**: Let $\mu$ be a probability measure on $\mathbb{R}^d$ and $\mu_N$ its empirical measure with sample size $N$. We prove a concentration inequality for the optimal transport cost between $\mu$ and $\mu_N$ for cost functions with polynomial local growth, that can have superpolynomial global growth. This result generalizes and improves upon estimates of Fournier and Guillin. By partitioning $\mathbb{R}^d$ into annuli, we infer a global estimate from local estimates on the annuli and conclude that the global estimate can be expressed as a sum of the local estimate and a mean-deviation probability for which efficient bounds are known. This talk is based on joint work with Martin Larsson and Jonghwa Park.

**[05606] Adapted Wasserstein distance between the laws of SDEs****Format**: Online Talk on Zoom**Author(s)**:**Beatrice Acciaio**(ETH Zurich)- Sigrid Kallblad (KTH Royal Institute of Technology in Stockholm)

**Abstract**: We consider here an adapted optimal transport problem between the laws of Markovian stochastic differential equations (SDEs) and establish optimality of the so-called synchronous coupling between the given laws. The proof of this result is based on time-discretisation methods and reveals an interesting connection between the synchronous coupling and the celebrated discrete-time Knothe–Rosenblatt rearrangement. We also provide a result on equality of various topologies when restricting to certain types of laws of continuous-time processes. The talk is based on joint work with Julio Backhoff and Ben Robinson.

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