Maximum Principle for Stochastic Control System with Elephant Memory and Jump Diffusion
Motivated by a duopoly game problem, the authors study an optimal control problem where the system is driven by Brownian motion and Poisson point process and has elephant memory for the control variable and the state variable. Firstly, the authors establish the unique solvability of an anticipated b...
Gespeichert in:
| Veröffentlicht in: | Journal of systems science and complexity 2024-08, Vol.37 (4), p.1392-1412 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1412 |
|---|---|
| container_issue | 4 |
| container_start_page | 1392 |
| container_title | Journal of systems science and complexity |
| container_volume | 37 |
| creator | Feng, Siqi Gao, Lei Wang, Guangchen Xiao, Hua |
| description | Motivated by a duopoly game problem, the authors study an optimal control problem where the system is driven by Brownian motion and Poisson point process and has elephant memory for the control variable and the state variable. Firstly, the authors establish the unique solvability of an anticipated backward stochastic differential equation, derive a stochastic maximum principle, and prove a verification theorem for the aforementioned optimal control problem. Furthermore, the authors generalize these results to nonzero-sum stochastic differential game problems. Finally, the authors apply the theoretical results to the duopoly game problem and obtain the corresponding Nash equilibrium solution. |
| doi_str_mv | 10.1007/s11424-024-3163-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3066865332</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3066865332</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-d7c5b27d2e7ed4a44239575a5872ba61300b6ddd5a69a10fcf603519b0e57a8d3</originalsourceid><addsrcrecordid>eNp1kE1LxDAQhosouK7-AG8Bz9VJ0iTtUdZvdlFYxWNIm9TN0jY1SdH993ap4MnDMHN43nfgSZJzDJcYQFwFjDOSpTAOxZym4iCZYcaKVAAXh-MNUKQck-w4OQlhC0B5AfkseV-pb9sOLXrxtqts3xhUO4_W0VUbFaKt0MJ10bsGrXchmhZ92bhBt43pN6qLaGVa53dIdRo9DW2PbmxdD8G67jQ5qlUTzNnvnidvd7evi4d0-Xz_uLhephXheUy1qFhJhCZGGJ2pLCO0YIIplgtSKo4pQMm11kzxQmGoq5oDZbgowTChck3nycXU23v3OZgQ5dYNvhtfSgqc55xRSkYKT1TlXQje1LL3tlV-JzHIvT85-ZOjP7n3J8WYIVMmjGz3Yfxf8_-hH4xzctA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3066865332</pqid></control><display><type>article</type><title>Maximum Principle for Stochastic Control System with Elephant Memory and Jump Diffusion</title><source>Springer Nature - Complete Springer Journals</source><source>Alma/SFX Local Collection</source><creator>Feng, Siqi ; Gao, Lei ; Wang, Guangchen ; Xiao, Hua</creator><creatorcontrib>Feng, Siqi ; Gao, Lei ; Wang, Guangchen ; Xiao, Hua</creatorcontrib><description>Motivated by a duopoly game problem, the authors study an optimal control problem where the system is driven by Brownian motion and Poisson point process and has elephant memory for the control variable and the state variable. Firstly, the authors establish the unique solvability of an anticipated backward stochastic differential equation, derive a stochastic maximum principle, and prove a verification theorem for the aforementioned optimal control problem. Furthermore, the authors generalize these results to nonzero-sum stochastic differential game problems. Finally, the authors apply the theoretical results to the duopoly game problem and obtain the corresponding Nash equilibrium solution.</description><identifier>ISSN: 1009-6124</identifier><identifier>EISSN: 1559-7067</identifier><identifier>DOI: 10.1007/s11424-024-3163-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Complex Systems ; Control ; Control systems ; Differential equations ; Differential games ; Elephants ; Game theory ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Maximum principle ; Operations Research/Decision Theory ; Optimal control ; Statistics ; Stochastic processes ; Systems Theory</subject><ispartof>Journal of systems science and complexity, 2024-08, Vol.37 (4), p.1392-1412</ispartof><rights>The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2024</rights><rights>The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2024.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-d7c5b27d2e7ed4a44239575a5872ba61300b6ddd5a69a10fcf603519b0e57a8d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11424-024-3163-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11424-024-3163-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Feng, Siqi</creatorcontrib><creatorcontrib>Gao, Lei</creatorcontrib><creatorcontrib>Wang, Guangchen</creatorcontrib><creatorcontrib>Xiao, Hua</creatorcontrib><title>Maximum Principle for Stochastic Control System with Elephant Memory and Jump Diffusion</title><title>Journal of systems science and complexity</title><addtitle>J Syst Sci Complex</addtitle><description>Motivated by a duopoly game problem, the authors study an optimal control problem where the system is driven by Brownian motion and Poisson point process and has elephant memory for the control variable and the state variable. Firstly, the authors establish the unique solvability of an anticipated backward stochastic differential equation, derive a stochastic maximum principle, and prove a verification theorem for the aforementioned optimal control problem. Furthermore, the authors generalize these results to nonzero-sum stochastic differential game problems. Finally, the authors apply the theoretical results to the duopoly game problem and obtain the corresponding Nash equilibrium solution.</description><subject>Complex Systems</subject><subject>Control</subject><subject>Control systems</subject><subject>Differential equations</subject><subject>Differential games</subject><subject>Elephants</subject><subject>Game theory</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Maximum principle</subject><subject>Operations Research/Decision Theory</subject><subject>Optimal control</subject><subject>Statistics</subject><subject>Stochastic processes</subject><subject>Systems Theory</subject><issn>1009-6124</issn><issn>1559-7067</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAQhosouK7-AG8Bz9VJ0iTtUdZvdlFYxWNIm9TN0jY1SdH993ap4MnDMHN43nfgSZJzDJcYQFwFjDOSpTAOxZym4iCZYcaKVAAXh-MNUKQck-w4OQlhC0B5AfkseV-pb9sOLXrxtqts3xhUO4_W0VUbFaKt0MJ10bsGrXchmhZ92bhBt43pN6qLaGVa53dIdRo9DW2PbmxdD8G67jQ5qlUTzNnvnidvd7evi4d0-Xz_uLhephXheUy1qFhJhCZGGJ2pLCO0YIIplgtSKo4pQMm11kzxQmGoq5oDZbgowTChck3nycXU23v3OZgQ5dYNvhtfSgqc55xRSkYKT1TlXQje1LL3tlV-JzHIvT85-ZOjP7n3J8WYIVMmjGz3Yfxf8_-hH4xzctA</recordid><startdate>20240801</startdate><enddate>20240801</enddate><creator>Feng, Siqi</creator><creator>Gao, Lei</creator><creator>Wang, Guangchen</creator><creator>Xiao, Hua</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240801</creationdate><title>Maximum Principle for Stochastic Control System with Elephant Memory and Jump Diffusion</title><author>Feng, Siqi ; Gao, Lei ; Wang, Guangchen ; Xiao, Hua</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-d7c5b27d2e7ed4a44239575a5872ba61300b6ddd5a69a10fcf603519b0e57a8d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Complex Systems</topic><topic>Control</topic><topic>Control systems</topic><topic>Differential equations</topic><topic>Differential games</topic><topic>Elephants</topic><topic>Game theory</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Maximum principle</topic><topic>Operations Research/Decision Theory</topic><topic>Optimal control</topic><topic>Statistics</topic><topic>Stochastic processes</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Feng, Siqi</creatorcontrib><creatorcontrib>Gao, Lei</creatorcontrib><creatorcontrib>Wang, Guangchen</creatorcontrib><creatorcontrib>Xiao, Hua</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of systems science and complexity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Feng, Siqi</au><au>Gao, Lei</au><au>Wang, Guangchen</au><au>Xiao, Hua</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Maximum Principle for Stochastic Control System with Elephant Memory and Jump Diffusion</atitle><jtitle>Journal of systems science and complexity</jtitle><stitle>J Syst Sci Complex</stitle><date>2024-08-01</date><risdate>2024</risdate><volume>37</volume><issue>4</issue><spage>1392</spage><epage>1412</epage><pages>1392-1412</pages><issn>1009-6124</issn><eissn>1559-7067</eissn><abstract>Motivated by a duopoly game problem, the authors study an optimal control problem where the system is driven by Brownian motion and Poisson point process and has elephant memory for the control variable and the state variable. Firstly, the authors establish the unique solvability of an anticipated backward stochastic differential equation, derive a stochastic maximum principle, and prove a verification theorem for the aforementioned optimal control problem. Furthermore, the authors generalize these results to nonzero-sum stochastic differential game problems. Finally, the authors apply the theoretical results to the duopoly game problem and obtain the corresponding Nash equilibrium solution.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s11424-024-3163-7</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1009-6124 |
| ispartof | Journal of systems science and complexity, 2024-08, Vol.37 (4), p.1392-1412 |
| issn | 1009-6124 1559-7067 |
| language | eng |
| recordid | cdi_proquest_journals_3066865332 |
| source | Springer Nature - Complete Springer Journals; Alma/SFX Local Collection |
| subjects | Complex Systems Control Control systems Differential equations Differential games Elephants Game theory Mathematics Mathematics and Statistics Mathematics of Computing Maximum principle Operations Research/Decision Theory Optimal control Statistics Stochastic processes Systems Theory |
| title | Maximum Principle for Stochastic Control System with Elephant Memory and Jump Diffusion |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-13T20%3A43%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Maximum%20Principle%20for%20Stochastic%20Control%20System%20with%20Elephant%20Memory%20and%20Jump%20Diffusion&rft.jtitle=Journal%20of%20systems%20science%20and%20complexity&rft.au=Feng,%20Siqi&rft.date=2024-08-01&rft.volume=37&rft.issue=4&rft.spage=1392&rft.epage=1412&rft.pages=1392-1412&rft.issn=1009-6124&rft.eissn=1559-7067&rft_id=info:doi/10.1007/s11424-024-3163-7&rft_dat=%3Cproquest_cross%3E3066865332%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3066865332&rft_id=info:pmid/&rfr_iscdi=true |