Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916426023960576 |
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| author | Davey, Ashley Zheng, Harry |
| author_facet | Davey, Ashley Zheng, Harry |
| contents | We consider the portfolio optimisation problem where the terminal function is an S-shaped utility applied at the difference between the wealth and a random benchmark process. We develop several numerical methods for solving the problem using deep learning and duality methods. We use deep learning methods to solve the associated Hamilton-Jacobi-Bellman equation for both the primal and dual problems, and the adjoint equation arising from the stochastic maximum principle. We compare the solution of this non-concave problem to that of concavified utility, a random function depending on the benchmark, in both complete and incomplete markets. We give some numerical results for power and log utilities to show the accuracy of the suggested algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point Davey, Ashley Zheng, Harry Computational Finance Optimization and Control Machine Learning We consider the portfolio optimisation problem where the terminal function is an S-shaped utility applied at the difference between the wealth and a random benchmark process. We develop several numerical methods for solving the problem using deep learning and duality methods. We use deep learning methods to solve the associated Hamilton-Jacobi-Bellman equation for both the primal and dual problems, and the adjoint equation arising from the stochastic maximum principle. We compare the solution of this non-concave problem to that of concavified utility, a random function depending on the benchmark, in both complete and incomplete markets. We give some numerical results for power and log utilities to show the accuracy of the suggested algorithms. |
| title | Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point |
| topic | Computational Finance Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2410.05524 |