Constrained LQ Problem with a Random Jump and Application to Portfolio Selection
This paper deals with a constrained stochastic linear-quadratic (LQ for short) optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical...
Gespeichert in:
| Veröffentlicht in: | Chinese annals of mathematics. Serie B 2018-09, Vol.39 (5), p.829-848 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 848 |
|---|---|
| container_issue | 5 |
| container_start_page | 829 |
| container_title | Chinese annals of mathematics. Serie B |
| container_volume | 39 |
| creator | Dong, Yuchao |
| description | This paper deals with a constrained stochastic linear-quadratic (LQ for short) optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Itô-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations (BSDEs for short). The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty. |
| doi_str_mv | 10.1007/s11401-018-0099-z |
| format | Article |
| fullrecord | <record><control><sourceid>wanfang_jour_proqu</sourceid><recordid>TN_cdi_wanfang_journals_sxnk_e201805005</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><wanfj_id>sxnk_e201805005</wanfj_id><sourcerecordid>sxnk_e201805005</sourcerecordid><originalsourceid>FETCH-LOGICAL-c348t-7d218838812a475cfcf98dc9652fcadfd1c352ff26a2ffbf2915ad61d6896083</originalsourceid><addsrcrecordid>eNp1kMtOwzAQRS0EEqXwAewssWAVmHGa1F5WFU9VokD3luvYEEjtYKfi8fU4ClJXbGZGo3PvjC4hpwgXCDC9jIgTwAyQZwBCZD97ZIS8hKxkJe6TEbCCZaIQ4pAcxfgGgJNpASOynHsXu6BqZyq6eKTL4NeN2dDPunulij4pV_kNvd9uWppGOmvbptaqq72jnadLHzrrm9rTZ9MY3a-PyYFVTTQnf31MVtdXq_lttni4uZvPFpnOJ7zLphVDznPOkan0ibbaCl5pURbMalXZCnWeRstKleraMoGFqkqsSi5K4PmYnA-2n8pZ5V7km98Glw7K-OXepWEpCSgAikSeDWQb_MfWxG6HMkSR57nA3g8HSgcfYzBWtqHeqPAtEWSfsBwSlslX9gnLn6RhgyYm1r2YsHP-X_QLTUp93A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2119333918</pqid></control><display><type>article</type><title>Constrained LQ Problem with a Random Jump and Application to Portfolio Selection</title><source>Springer Nature - Complete Springer Journals</source><source>Alma/SFX Local Collection</source><creator>Dong, Yuchao</creator><creatorcontrib>Dong, Yuchao</creatorcontrib><description>This paper deals with a constrained stochastic linear-quadratic (LQ for short) optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Itô-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations (BSDEs for short). The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.</description><identifier>ISSN: 0252-9599</identifier><identifier>EISSN: 1860-6261</identifier><identifier>DOI: 10.1007/s11401-018-0099-z</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Differential equations ; Economic models ; Markov analysis ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Optimal control</subject><ispartof>Chinese annals of mathematics. Serie B, 2018-09, Vol.39 (5), p.829-848</ispartof><rights>Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><rights>Copyright © Wanfang Data Co. Ltd. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c348t-7d218838812a475cfcf98dc9652fcadfd1c352ff26a2ffbf2915ad61d6896083</citedby><cites>FETCH-LOGICAL-c348t-7d218838812a475cfcf98dc9652fcadfd1c352ff26a2ffbf2915ad61d6896083</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://www.wanfangdata.com.cn/images/PeriodicalImages/sxnk-e/sxnk-e.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11401-018-0099-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11401-018-0099-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Dong, Yuchao</creatorcontrib><title>Constrained LQ Problem with a Random Jump and Application to Portfolio Selection</title><title>Chinese annals of mathematics. Serie B</title><addtitle>Chin. Ann. Math. Ser. B</addtitle><description>This paper deals with a constrained stochastic linear-quadratic (LQ for short) optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Itô-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations (BSDEs for short). The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.</description><subject>Applications of Mathematics</subject><subject>Differential equations</subject><subject>Economic models</subject><subject>Markov analysis</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimal control</subject><issn>0252-9599</issn><issn>1860-6261</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRS0EEqXwAewssWAVmHGa1F5WFU9VokD3luvYEEjtYKfi8fU4ClJXbGZGo3PvjC4hpwgXCDC9jIgTwAyQZwBCZD97ZIS8hKxkJe6TEbCCZaIQ4pAcxfgGgJNpASOynHsXu6BqZyq6eKTL4NeN2dDPunulij4pV_kNvd9uWppGOmvbptaqq72jnadLHzrrm9rTZ9MY3a-PyYFVTTQnf31MVtdXq_lttni4uZvPFpnOJ7zLphVDznPOkan0ibbaCl5pURbMalXZCnWeRstKleraMoGFqkqsSi5K4PmYnA-2n8pZ5V7km98Glw7K-OXepWEpCSgAikSeDWQb_MfWxG6HMkSR57nA3g8HSgcfYzBWtqHeqPAtEWSfsBwSlslX9gnLn6RhgyYm1r2YsHP-X_QLTUp93A</recordid><startdate>20180901</startdate><enddate>20180901</enddate><creator>Dong, Yuchao</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>Department of Mathematics, Fudan University, Shanghai 200433, China</general><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20180901</creationdate><title>Constrained LQ Problem with a Random Jump and Application to Portfolio Selection</title><author>Dong, Yuchao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c348t-7d218838812a475cfcf98dc9652fcadfd1c352ff26a2ffbf2915ad61d6896083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applications of Mathematics</topic><topic>Differential equations</topic><topic>Economic models</topic><topic>Markov analysis</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Optimal control</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dong, Yuchao</creatorcontrib><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Chinese annals of mathematics. Serie B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dong, Yuchao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Constrained LQ Problem with a Random Jump and Application to Portfolio Selection</atitle><jtitle>Chinese annals of mathematics. Serie B</jtitle><stitle>Chin. Ann. Math. Ser. B</stitle><date>2018-09-01</date><risdate>2018</risdate><volume>39</volume><issue>5</issue><spage>829</spage><epage>848</epage><pages>829-848</pages><issn>0252-9599</issn><eissn>1860-6261</eissn><abstract>This paper deals with a constrained stochastic linear-quadratic (LQ for short) optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Itô-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations (BSDEs for short). The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s11401-018-0099-z</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0252-9599 |
| ispartof | Chinese annals of mathematics. Serie B, 2018-09, Vol.39 (5), p.829-848 |
| issn | 0252-9599 1860-6261 |
| language | eng |
| recordid | cdi_wanfang_journals_sxnk_e201805005 |
| source | Springer Nature - Complete Springer Journals; Alma/SFX Local Collection |
| subjects | Applications of Mathematics Differential equations Economic models Markov analysis Mathematical analysis Mathematics Mathematics and Statistics Optimal control |
| title | Constrained LQ Problem with a Random Jump and Application to Portfolio Selection |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-31T21%3A19%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wanfang_jour_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Constrained%20LQ%20Problem%20with%20a%20Random%20Jump%20and%20Application%20to%20Portfolio%20Selection&rft.jtitle=Chinese%20annals%20of%20mathematics.%20Serie%20B&rft.au=Dong,%20Yuchao&rft.date=2018-09-01&rft.volume=39&rft.issue=5&rft.spage=829&rft.epage=848&rft.pages=829-848&rft.issn=0252-9599&rft.eissn=1860-6261&rft_id=info:doi/10.1007/s11401-018-0099-z&rft_dat=%3Cwanfang_jour_proqu%3Esxnk_e201805005%3C/wanfang_jour_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2119333918&rft_id=info:pmid/&rft_wanfj_id=sxnk_e201805005&rfr_iscdi=true |