Fredholm Approach to Nonlinear Propagator Models
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912262431703040 |
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| author | Jaber, Eduardo Abi Bondi, Alessandro De Carvalho, Nathan Neuman, Eyal Tuschmann, Sturmius |
| author_facet | Jaber, Eduardo Abi Bondi, Alessandro De Carvalho, Nathan Neuman, Eyal Tuschmann, Sturmius |
| contents | We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we demonstrate that the optimal trading strategy satisfies a nonlinear stochastic Fredholm equation with both forward and backward coefficients. We prove the existence and uniqueness of the solution under a monotonicity condition reflecting the nonlinearity of the price impact. Moreover, we derive an existence result for the optimal strategy beyond this condition when the underlying probability space is countable. In addition, we introduce a novel iterative scheme and establish its convergence to the optimal trading strategy. Finally, we provide a numerical implementation of the scheme that illustrates its convergence, stability, and the effects of concavity on optimal execution strategies under exponential and power-law decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fredholm Approach to Nonlinear Propagator Models Jaber, Eduardo Abi Bondi, Alessandro De Carvalho, Nathan Neuman, Eyal Tuschmann, Sturmius Mathematical Finance Optimization and Control Trading and Market Microstructure 93E20, 60H30, 91G80 We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we demonstrate that the optimal trading strategy satisfies a nonlinear stochastic Fredholm equation with both forward and backward coefficients. We prove the existence and uniqueness of the solution under a monotonicity condition reflecting the nonlinearity of the price impact. Moreover, we derive an existence result for the optimal strategy beyond this condition when the underlying probability space is countable. In addition, we introduce a novel iterative scheme and establish its convergence to the optimal trading strategy. Finally, we provide a numerical implementation of the scheme that illustrates its convergence, stability, and the effects of concavity on optimal execution strategies under exponential and power-law decay. |
| title | Fredholm Approach to Nonlinear Propagator Models |
| topic | Mathematical Finance Optimization and Control Trading and Market Microstructure 93E20, 60H30, 91G80 |
| url | https://arxiv.org/abs/2503.04323 |