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Fundamental properties of process distances

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  • Veraguas, Julio Backhoff
  • Beiglböck, Mathias
  • Eder, Manu
  • Pichler, Alois

Abstract

To quantify the difference of distinct stochastic processes it is not sufficient to consider the distance of their states and corresponding probabilities. Instead, the information, which evolves and accumulates over time and which is mathematically encoded by filtrations, has to be accounted for as well. The nested distance, also known as bicausal Wasserstein distance, recognizes this component and involves the filtration properly. This distance is of emerging importance due to its applications in stochastic analysis, stochastic programming, mathematical economics and other disciplines.

Suggested Citation

  • Veraguas, Julio Backhoff & Beiglböck, Mathias & Eder, Manu & Pichler, Alois, 2020. "Fundamental properties of process distances," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5575-5591.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5575-5591
    DOI: 10.1016/j.spa.2020.03.017
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    References listed on IDEAS

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    Cited by:

    1. Ruslan Mirmominov & Johannes Wiesel, 2024. "A dynamic programming principle for multiperiod control problems with bicausal constraints," Papers 2410.23927, arXiv.org.
    2. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    3. Mathias Beiglbock & Benjamin Jourdain & William Margheriti & Gudmund Pammer, 2021. "Stability of the Weak Martingale Optimal Transport Problem," Papers 2109.06322, arXiv.org, revised Apr 2022.

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