The perturbation method applied to a robust optimization problem with constraint
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929242051182592 |
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| author | Luo, Peng Schied, Alexander Xue, Xiaole |
| author_facet | Luo, Peng Schied, Alexander Xue, Xiaole |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The perturbation method applied to a robust optimization problem with constraint Luo, Peng Schied, Alexander Xue, Xiaole Optimization and Control Probability 93E20, 60H10, 35K15 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. |
| title | The perturbation method applied to a robust optimization problem with constraint |
| topic | Optimization and Control Probability 93E20, 60H10, 35K15 |
| url | https://arxiv.org/abs/2402.08260 |