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Convergence of adapted smoothed empirical measures

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  • Hou, Songyan

Abstract

The adapted Wasserstein distance (AW-distance) controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the AW-distance are bottlenecked by the failure of empirical measures (Emp) to converge under this distance. Kernel smoothing and adapted projection have been introduced to construct converging substitutes of empirical measures, known respectively as smoothed empirical measures (S-Emp) and adapted empirical measures (A-Emp). However, both approaches have limitations. Specifically, S-Emp lack comprehensive convergence results, whereas A-Emp in practical applications lead to fewer distinct samples compared to standard empirical measures.

Suggested Citation

  • Hou, Songyan, 2026. "Convergence of adapted smoothed empirical measures," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002194
    DOI: 10.1016/j.spa.2025.104775
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    References listed on IDEAS

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    1. 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.
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    3. Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," LSE Research Online Documents on Economics 101864, London School of Economics and Political Science, LSE Library.
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    5. Dedecker, Jérôme & Fan, Xiequan, 2015. "Deviation inequalities for separately Lipschitz functionals of iterated random functions," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 60-90.
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