Stochastic maximum principle for problems with delay with general dependence on the past
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866917611978096640 |
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| author | Guatteri, Giuseppina Masiero, Federica |
| author_facet | Guatteri, Giuseppina Masiero, Federica |
| contents | We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and also the final cost functional may depend on the past trajectories. The adjoint equations turn out to be a new form of linear anticipated backward stochastic differential equations (ABSDEs in the following), and we prove a direct formula to solve these equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_03953 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Stochastic maximum principle for problems with delay with general dependence on the past Guatteri, Giuseppina Masiero, Federica Probability 60H10, 93E20 We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and also the final cost functional may depend on the past trajectories. The adjoint equations turn out to be a new form of linear anticipated backward stochastic differential equations (ABSDEs in the following), and we prove a direct formula to solve these equations. |
| title | Stochastic maximum principle for problems with delay with general dependence on the past |
| topic | Probability 60H10, 93E20 |
| url | https://arxiv.org/abs/2002.03953 |