Sensitivity of Multiperiod Optimization Problems with Respect to the Adapted Wasserstein Distance

Daniel Bartl; Johannes Wiesel

doi:https://doi.org/10.1137/22M1537746

Sensitivity of Multiperiod Optimization Problems with Respect to the Adapted Wasserstein Distance

Daniel Bartl, Johannes Wiesel (Corresponding author)

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We analyze the effect of small changes in the underlying probabilistic model on the value of multiperiod stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the adapted Wasserstein distance. We prove explicit first-order approximations for both problems. Expected utility maximization is discussed as a special case.

Original language	English
Pages (from-to)	704 - 720
Number of pages	17
Journal	SIAM Journal on Financial Mathematics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1137/22M1537746
Publication status	Published - 2023

Austrian Fields of Science 2012

101024 Probability theory
101007 Financial mathematics

Keywords

(adapted) Wasserstein distance
optimal stopping
robust multiperiod stochastic optimization
sensitivity analysis

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https://doi.org/10.1137/22M1537746

Cite this

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title = "Sensitivity of Multiperiod Optimization Problems with Respect to the Adapted Wasserstein Distance",

abstract = "We analyze the effect of small changes in the underlying probabilistic model on the value of multiperiod stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the adapted Wasserstein distance. We prove explicit first-order approximations for both problems. Expected utility maximization is discussed as a special case.",

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AB - We analyze the effect of small changes in the underlying probabilistic model on the value of multiperiod stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the adapted Wasserstein distance. We prove explicit first-order approximations for both problems. Expected utility maximization is discussed as a special case.

KW - (adapted) Wasserstein distance

KW - optimal stopping

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KW - sensitivity analysis

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DO - https://doi.org/10.1137/22M1537746

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JF - SIAM Journal on Financial Mathematics

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ER -

Sensitivity of Multiperiod Optimization Problems with Respect to the Adapted Wasserstein Distance

Abstract

Austrian Fields of Science 2012

Keywords

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