S-shaped Utility Maximization with VaR Constraint and Partial Information
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915338136846336 |
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| author | Zhu, Dongmei Davey, Ashley Zheng, Harry |
| author_facet | Zhu, Dongmei Davey, Ashley Zheng, Harry |
| contents | We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determines if the constrained problem admits a unique optimal solution and Lagrange multiplier or is infeasible. We also propose three algorithms (Lagrange, simulation, deep neural network) to solve the problem and compare their performances with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | S-shaped Utility Maximization with VaR Constraint and Partial Information Zhu, Dongmei Davey, Ashley Zheng, Harry Mathematical Finance Optimization and Control 93E20, 93E11, 91G80, 90C46, 49M29 We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determines if the constrained problem admits a unique optimal solution and Lagrange multiplier or is infeasible. We also propose three algorithms (Lagrange, simulation, deep neural network) to solve the problem and compare their performances with numerical examples. |
| title | S-shaped Utility Maximization with VaR Constraint and Partial Information |
| topic | Mathematical Finance Optimization and Control 93E20, 93E11, 91G80, 90C46, 49M29 |
| url | https://arxiv.org/abs/2506.10103 |