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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.19571 |
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| _version_ | 1866909328908222464 |
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| author | Guan, Guohui Jia, Yuting Liang, Zongxia |
| author_facet | Guan, Guohui Jia, Yuting Liang, Zongxia |
| contents | This paper studies the robust portfolio selection problem under a state-dependent confidence set. The investor invests in a financial market with a risk-free asset and a risky asset. The ambiguity-averse investor faces uncertainty over the drift of the risky asset and updates posterior beliefs by Bayesian learning. The investor holds the belief that the unknown drift falls within a confidence set at a certain confidence level. The confidence set varies with both the observed state and time. By maximizing the expected CARA utility of terminal wealth under the worst-case scenario of the unknown drift, we derive and solve the associated HJBI equation. The robust optimal investment strategy is obtained in a semi-analytical form based on a PDE. We validate the existence and uniqueness of the PDE and demonstrate the optimality of the solution in the verification theorem. The robust optimal investment strategy consists of two components: myopic demand in the worst-case scenario and hedging demand. The robust optimal investment strategy is categorized into three regions: buying, selling, and small trading. Ambiguity aversion results in a more conservative robust optimal investment strategy. Additionally, with learning, the investor's uncertainty about the drift decreases over time, leading to increased risk exposure to the risky asset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Portfolio Selection under State-dependent Confidence Set Guan, Guohui Jia, Yuting Liang, Zongxia Optimization and Control 91B28, 49L20, 91B16, 91B70 This paper studies the robust portfolio selection problem under a state-dependent confidence set. The investor invests in a financial market with a risk-free asset and a risky asset. The ambiguity-averse investor faces uncertainty over the drift of the risky asset and updates posterior beliefs by Bayesian learning. The investor holds the belief that the unknown drift falls within a confidence set at a certain confidence level. The confidence set varies with both the observed state and time. By maximizing the expected CARA utility of terminal wealth under the worst-case scenario of the unknown drift, we derive and solve the associated HJBI equation. The robust optimal investment strategy is obtained in a semi-analytical form based on a PDE. We validate the existence and uniqueness of the PDE and demonstrate the optimality of the solution in the verification theorem. The robust optimal investment strategy consists of two components: myopic demand in the worst-case scenario and hedging demand. The robust optimal investment strategy is categorized into three regions: buying, selling, and small trading. Ambiguity aversion results in a more conservative robust optimal investment strategy. Additionally, with learning, the investor's uncertainty about the drift decreases over time, leading to increased risk exposure to the risky asset. |
| title | Robust Portfolio Selection under State-dependent Confidence Set |
| topic | Optimization and Control 91B28, 49L20, 91B16, 91B70 |
| url | https://arxiv.org/abs/2409.19571 |