A Global Stochastic Maximum Principle for Mean-Field Forward-Backward Stochastic Control Systems with Quadratic Generators
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913308503703552 |
|---|---|
| author | Buckdahn, Rainer Li, Juan Li, Yanwei Wang, Yi |
| author_facet | Buckdahn, Rainer Li, Juan Li, Yanwei Wang, Yi |
| contents | Our paper is devoted to the study of Peng's stochastic maximum principle (SMP) for a stochastic control problem composed of a controlled forward stochastic differential equation (SDE) as dynamics and a controlled backward SDE which defines the cost functional. Our studies combine the difficulties which come, on one hand, from the fact that the coefficients of both the SDE and the backward SDE are of mean-field type (i.e., they do not only depend on the control process and the solution processes but also on their law), and on the other hand, from the fact that the coefficient of the BSDE is of quadratic growth in $Z$. Our SMP is novel, it extends in a by far non trivial way existing results on SMP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Global Stochastic Maximum Principle for Mean-Field Forward-Backward Stochastic Control Systems with Quadratic Generators Buckdahn, Rainer Li, Juan Li, Yanwei Wang, Yi Optimization and Control Our paper is devoted to the study of Peng's stochastic maximum principle (SMP) for a stochastic control problem composed of a controlled forward stochastic differential equation (SDE) as dynamics and a controlled backward SDE which defines the cost functional. Our studies combine the difficulties which come, on one hand, from the fact that the coefficients of both the SDE and the backward SDE are of mean-field type (i.e., they do not only depend on the control process and the solution processes but also on their law), and on the other hand, from the fact that the coefficient of the BSDE is of quadratic growth in $Z$. Our SMP is novel, it extends in a by far non trivial way existing results on SMP. |
| title | A Global Stochastic Maximum Principle for Mean-Field Forward-Backward Stochastic Control Systems with Quadratic Generators |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.06826 |