Mind the jumps: when 2BSDEs meet semi-martingales
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918080183009280 |
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| author | Possamaï, Dylan Rodrigues, Marco Saplaouras, Alexandros |
| author_facet | Possamaï, Dylan Rodrigues, Marco Saplaouras, Alexandros |
| contents | We construct an aggregated version of the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs). The results can be applied to control problems where the triplet of semi-martingale characteristics is controlled in a possibly non-dominated case or where uncertainty about the characteristics is present in the optimisation. The construction also provides a time-consistent system of fully nonlinear conditional expectations on the Skorokhod space. We find the semi-martingale decomposition of the value function and characterise it as the solution to a semi-martingale second-order BSDE. The generality we seek allows for the treatment of controlled diffusions, pure-jump processes, and discrete-time processes in a unified setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01767 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mind the jumps: when 2BSDEs meet semi-martingales Possamaï, Dylan Rodrigues, Marco Saplaouras, Alexandros Probability Optimization and Control 60G44, 60G57, 60H05, 60H10, 60H20, 93E20 We construct an aggregated version of the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs). The results can be applied to control problems where the triplet of semi-martingale characteristics is controlled in a possibly non-dominated case or where uncertainty about the characteristics is present in the optimisation. The construction also provides a time-consistent system of fully nonlinear conditional expectations on the Skorokhod space. We find the semi-martingale decomposition of the value function and characterise it as the solution to a semi-martingale second-order BSDE. The generality we seek allows for the treatment of controlled diffusions, pure-jump processes, and discrete-time processes in a unified setting. |
| title | Mind the jumps: when 2BSDEs meet semi-martingales |
| topic | Probability Optimization and Control 60G44, 60G57, 60H05, 60H10, 60H20, 93E20 |
| url | https://arxiv.org/abs/2507.01767 |