Social Optima of Linear Forward-Backward Stochastic System
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914774260908032 |
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| author | Wang, Guangchen Wang, Shujun Xiong, Jie |
| author_facet | Wang, Guangchen Wang, Shujun Xiong, Jie |
| contents | A linear quadratic (LQ) stochastic optimization system involving large population, which is driven by forward-backward stochastic differential equation (FBSDE), is investigated in this paper. Agents cooperate with each other to minimize the so-called social objective, which is rather different from mean field (MF) game. Employing forward-backward person-by-person optimality principle, we derive an auxiliary LQ control problem by decentralized information. A decentralized strategy is obtained by virtue of an MF-type forward-backward stochastic differential equation consistency condition. Applying Riccati equation decoupling method, we solve the consistency condition system. We also verify the asymptotic social optimality in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Social Optima of Linear Forward-Backward Stochastic System Wang, Guangchen Wang, Shujun Xiong, Jie Optimization and Control A linear quadratic (LQ) stochastic optimization system involving large population, which is driven by forward-backward stochastic differential equation (FBSDE), is investigated in this paper. Agents cooperate with each other to minimize the so-called social objective, which is rather different from mean field (MF) game. Employing forward-backward person-by-person optimality principle, we derive an auxiliary LQ control problem by decentralized information. A decentralized strategy is obtained by virtue of an MF-type forward-backward stochastic differential equation consistency condition. Applying Riccati equation decoupling method, we solve the consistency condition system. We also verify the asymptotic social optimality in this framework. |
| title | Social Optima of Linear Forward-Backward Stochastic System |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.18561 |