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Erscheinungsjahr: 
2022
Quellenangabe: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 26 [Issue:] 3 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 461-503
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
In this work, we consider optimal stopping problems with model uncertainty incorporated into the formulation of the underlying objective function. Typically, the robust, efficient hedging of American options in incomplete markets may be described as optimal stopping of such kind. Based on a generalisation of the additive dual representation of Rogers (Math. Financ. 12:271–286, 30 ) to the case of optimal stopping under model uncertainty, we develop a novel regression-based Monte Carlo algorithm for the approximation of the corresponding value function. The algorithm involves optimising a penalised empirical dual objective functional over a class of martingales. This formulation allows us to construct upper bounds for the optimal value with reduced complexity. Finally, we carry out a convergence analysis of the proposed algorithm and illustrate its performance by several numerical examples.
Schlagwörter: 
Model uncertainty
Optimal stopping
Dual representation
Empirical dual optimisation
Generative models
Covering numbers
Concentration inequalities
JEL: 
C73
G12
D81
Persistent Identifier der Erstveröffentlichung: 
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Dokumentart: 
Article
Dokumentversion: 
Published Version

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