The randomization method in stochastic optimal control
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912423629291520 |
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| author | Fuhrman, Marco |
| author_facet | Fuhrman, Marco |
| contents | In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic differential equation (BSDE), by means of an auxiliary optimization problem having the same value as the starting one. This method works for a large class of control problems and provides a BSDE representation to many related PDEs of Hamilton-Jacobi-Bellman type, even in the fully non linear case. After a general informal introduction we explain the method giving full details in a basic case. Then we try to give a complete picture of the existing applications and we present some related open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The randomization method in stochastic optimal control Fuhrman, Marco Optimization and Control Probability 60H10, 93E20 In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic differential equation (BSDE), by means of an auxiliary optimization problem having the same value as the starting one. This method works for a large class of control problems and provides a BSDE representation to many related PDEs of Hamilton-Jacobi-Bellman type, even in the fully non linear case. After a general informal introduction we explain the method giving full details in a basic case. Then we try to give a complete picture of the existing applications and we present some related open problems. |
| title | The randomization method in stochastic optimal control |
| topic | Optimization and Control Probability 60H10, 93E20 |
| url | https://arxiv.org/abs/2502.06356 |