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Mathematics and Financial Economics

18.03.2024 | Original Article

The perturbation method applied to a robust optimization problem with constraint

verfasst von: Peng Luo, Alexander Schied, Xiaole Xue

Erschienen in: Mathematics and Financial Economics

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Abstract

The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the optimal solution using a terminal perturbation method and properties of Bounded Mean Oscillation (BMO) martingales. The necessary condition is further proved to be sufficient for the existence of an optimal solution under an additional convexity assumption. Finally, the optimality condition is applied to discuss problems of partial hedging with ambiguity, fundraising under ambiguity and randomized testing problems for a quadratic g-expectation.

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Titel: The perturbation method applied to a robust optimization problem with constraint
verfasst von: Peng Luo
Alexander Schied
Xiaole Xue
Publikationsdatum: 18.03.2024
Verlag: Springer Berlin Heidelberg
Erschienen in: Mathematics and Financial Economics
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-024-00358-y