Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance
Considering the mind of rivalry between families, each family focuses not only on its own wealth but also on other families, especially neighbors. In this paper, we investigate the non-zero-sum mean-variance game between two families with a random household expenditure under the default risk and rel...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/1274649 |
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| _version_ | 1832549207834099712 |
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| author | Wenjin Guan Wei Yuan Sheng Li |
| author_facet | Wenjin Guan Wei Yuan Sheng Li |
| author_sort | Wenjin Guan |
| collection | DOAJ |
| description | Considering the mind of rivalry between families, each family focuses not only on its own wealth but also on other families, especially neighbors. In this paper, we investigate the non-zero-sum mean-variance game between two families with a random household expenditure under the default risk and relative performance. Applying the stochastic control theory within the framework of the game theory, the extended Hamilton–Jacobi–Bellman equation equations are derived. By solving this equation, we obtain the Nash equilibrium strategies of the two families and the corresponding equilibrium value functions. We also provide a numerical example to analyze the effects of relevant parameters on Nash equilibrium strategy and on the utility loss due to the mind of rivalry. |
| format | Article |
| id | doaj-art-f1f785cd5c9948f8950870c26cbcb5c9 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f1f785cd5c9948f8950870c26cbcb5c92025-02-03T06:11:56ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/12746491274649Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative PerformanceWenjin Guan0Wei Yuan1Sheng Li2Sichuan Administration Institute, Chengdu 610072, ChinaSichuan Administration Institute, Chengdu 610072, ChinaSchool of Statistics, Chengdu University of Information Technology, Chengdu 610103, ChinaConsidering the mind of rivalry between families, each family focuses not only on its own wealth but also on other families, especially neighbors. In this paper, we investigate the non-zero-sum mean-variance game between two families with a random household expenditure under the default risk and relative performance. Applying the stochastic control theory within the framework of the game theory, the extended Hamilton–Jacobi–Bellman equation equations are derived. By solving this equation, we obtain the Nash equilibrium strategies of the two families and the corresponding equilibrium value functions. We also provide a numerical example to analyze the effects of relevant parameters on Nash equilibrium strategy and on the utility loss due to the mind of rivalry.http://dx.doi.org/10.1155/2021/1274649 |
| spellingShingle | Wenjin Guan Wei Yuan Sheng Li Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance Complexity |
| title | Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance |
| title_full | Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance |
| title_fullStr | Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance |
| title_full_unstemmed | Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance |
| title_short | Optimal Time-Consistent Investment Strategy for a Random Household Expenditure with Default Risk under Relative Performance |
| title_sort | optimal time consistent investment strategy for a random household expenditure with default risk under relative performance |
| url | http://dx.doi.org/10.1155/2021/1274649 |
| work_keys_str_mv | AT wenjinguan optimaltimeconsistentinvestmentstrategyforarandomhouseholdexpenditurewithdefaultriskunderrelativeperformance AT weiyuan optimaltimeconsistentinvestmentstrategyforarandomhouseholdexpenditurewithdefaultriskunderrelativeperformance AT shengli optimaltimeconsistentinvestmentstrategyforarandomhouseholdexpenditurewithdefaultriskunderrelativeperformance |