Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application
Abstract This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a maximum principle and a verification theorem for the Nash equilibrium point by virtue of the duality an...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-12-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1438-1 |
| _version_ | 1817978485711306752 |
|---|---|
| author | Yi Zhuang |
| author_facet | Yi Zhuang |
| author_sort | Yi Zhuang |
| collection | DOAJ |
| description | Abstract This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a maximum principle and a verification theorem for the Nash equilibrium point by virtue of the duality and convex variation approach. We study a linear-quadratic system under partial information and present an explicit form of the Nash equilibrium point. We derive the filtering equations and prove the existence and uniqueness for the Nash equilibrium point. As an application, we solve a time-delayed pension fund management problem with nonlinear expectation to measure the risk and obtain the explicit solution. |
| first_indexed | 2024-04-13T22:30:00Z |
| format | Article |
| id | doaj.art-927603ccbc2543f49c7a7829d04c8740 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T22:30:00Z |
| publishDate | 2017-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-927603ccbc2543f49c7a7829d04c87402022-12-22T02:26:57ZengSpringerOpenAdvances in Difference Equations1687-18472017-12-012017112110.1186/s13662-017-1438-1Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and applicationYi Zhuang0School of Mathematics, Shandong UniversityAbstract This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a maximum principle and a verification theorem for the Nash equilibrium point by virtue of the duality and convex variation approach. We study a linear-quadratic system under partial information and present an explicit form of the Nash equilibrium point. We derive the filtering equations and prove the existence and uniqueness for the Nash equilibrium point. As an application, we solve a time-delayed pension fund management problem with nonlinear expectation to measure the risk and obtain the explicit solution.http://link.springer.com/article/10.1186/s13662-017-1438-1stochastic differential gamemaximum principlestochastic differential delayed equationlinear-quadratic problempartial informationg-expectation |
| spellingShingle | Yi Zhuang Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application Advances in Difference Equations stochastic differential game maximum principle stochastic differential delayed equation linear-quadratic problem partial information g-expectation |
| title | Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application |
| title_full | Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application |
| title_fullStr | Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application |
| title_full_unstemmed | Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application |
| title_short | Non-zero sum differential games of anticipated forward-backward stochastic differential delayed equations under partial information and application |
| title_sort | non zero sum differential games of anticipated forward backward stochastic differential delayed equations under partial information and application |
| topic | stochastic differential game maximum principle stochastic differential delayed equation linear-quadratic problem partial information g-expectation |
| url | http://link.springer.com/article/10.1186/s13662-017-1438-1 |
| work_keys_str_mv | AT yizhuang nonzerosumdifferentialgamesofanticipatedforwardbackwardstochasticdifferentialdelayedequationsunderpartialinformationandapplication |