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| The Stochastic Control Model for Use Conversion of Land* |
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Citation： |
Zhou YANG,Manni LV,Haisheng YANG.The Stochastic Control Model for Use Conversion of Land*[J].Chinese Annals of Mathematics B,2021,42(2):311~326 |
| Page view： 527
Net amount： 515 |
Authors： |
Zhou YANG; Manni LV;Haisheng YANG |
Foundation： |
National Natural Science Foundation of China (Nos. 11771158,11801091), the Guangdong Basic and Applied Basic Research Foundation (No. 2019A1515011338) and the Guangzhou Natural Science Found (No. 201904010189). |
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| Abstract： |
In this paper, the authors investigate the optimal conversion rate at which land use is irreversibly converted from biodiversity conservation to agricultural production. This problem is formulated as a stochastic control model, then transformed into a HJB equation involving free boundary. Since the state equation has singularity, it is difficult to directly derive the boundary value condition for the HJB equation. They provide a new method to overcome the difficulty via constructing another auxiliary stochastic control problem,and impose a proper boundary value condition. Moreover, they establish the existence and uniqueness of the viscosity solution of the HJB equation. Finally, they propose a stable numerical method for the HJB equation involving free boundary, and show some numerical results. |
Keywords： |
Optimal stochastic control, HJB equation, Free boundary, Land use |
Classification： |
93E20, 49L99, 49N90, 35Q99, 65N06 |
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