A stochastic linear-quadratic differential game with time-inconsistency
We consider a general stochastic linear-quadratic differential game with time-inconsistency. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different fr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-05-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022131?viewType=HTML |
| _version_ | 1811197785363447808 |
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| author | Qinglong Zhou Gaofeng Zong |
| author_facet | Qinglong Zhou Gaofeng Zong |
| author_sort | Qinglong Zhou |
| collection | DOAJ |
| description | We consider a general stochastic linear-quadratic differential game with time-inconsistency. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and derive a sufficient condition for equilibrium strategies via a system of forward-backward stochastic differential equation. When the state is one-dimensional and the coefficients are all deterministic, we find an explicit equilibrium strategy. The uniqueness of such equilibrium strategy is also given. |
| first_indexed | 2024-04-12T01:20:05Z |
| format | Article |
| id | doaj.art-bd0937f05b464da2b58478c7042be3aa |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-12T01:20:05Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-bd0937f05b464da2b58478c7042be3aa2022-12-22T03:53:50ZengAIMS PressElectronic Research Archive2688-15942022-05-013072550256710.3934/era.2022131A stochastic linear-quadratic differential game with time-inconsistencyQinglong Zhou0Gaofeng Zong11. Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China2. School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, ChinaWe consider a general stochastic linear-quadratic differential game with time-inconsistency. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and derive a sufficient condition for equilibrium strategies via a system of forward-backward stochastic differential equation. When the state is one-dimensional and the coefficients are all deterministic, we find an explicit equilibrium strategy. The uniqueness of such equilibrium strategy is also given.https://www.aimspress.com/article/doi/10.3934/era.2022131?viewType=HTMLtime-inconsistencystochastic linear-quadratic differential gameequilibrium strategybsdeforward-backward stochastic differential equation |
| spellingShingle | Qinglong Zhou Gaofeng Zong A stochastic linear-quadratic differential game with time-inconsistency Electronic Research Archive time-inconsistency stochastic linear-quadratic differential game equilibrium strategy bsde forward-backward stochastic differential equation |
| title | A stochastic linear-quadratic differential game with time-inconsistency |
| title_full | A stochastic linear-quadratic differential game with time-inconsistency |
| title_fullStr | A stochastic linear-quadratic differential game with time-inconsistency |
| title_full_unstemmed | A stochastic linear-quadratic differential game with time-inconsistency |
| title_short | A stochastic linear-quadratic differential game with time-inconsistency |
| title_sort | stochastic linear quadratic differential game with time inconsistency |
| topic | time-inconsistency stochastic linear-quadratic differential game equilibrium strategy bsde forward-backward stochastic differential equation |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022131?viewType=HTML |
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