{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:19:49Z","timestamp":1753881589470,"version":"3.41.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T00:00:00Z","timestamp":1630540800000},"content-version":"vor","delay-in-days":244,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008083","name":"Xihua University","doi-asserted-by":"publisher","award":["w202247"],"award-info":[{"award-number":["w202247"]}],"id":[{"id":"10.13039\/501100008083","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["JBK2101036"],"award-info":[{"award-number":["JBK2101036"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008006","name":"Yibin University","doi-asserted-by":"publisher","award":["2019QD07"],"award-info":[{"award-number":["2019QD07"]}],"id":[{"id":"10.13039\/501100008006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>When the market environment changes, we extend the self\u2010exciting price impact model and further analysis of investors\u2019 liquidation behaviour. It is assumed that the model is accompanied by an exponential decay factor when the temporary impact and its coefficient are linear and nonlinear. Using the optimal control method, we obtain that the optimal liquidation behaviours satisfy the second\u2010order nonlinear ODEs with variable coefficients in the case of linear and nonlinear temporary impact. Next, we solve the ODEs and get the form of the investors\u2019 optimal liquidation behaviour in four cases. Furthermore, we prove the decreasing properties of the optimal liquidation behaviour under the linear temporary impact. Through numerical simulation, we further explain the influence of the changed parameters <jats:italic>\u03c1<\/jats:italic>, <jats:italic>a<\/jats:italic>, <jats:italic>b<\/jats:italic>, <jats:italic>x<\/jats:italic>, and <jats:italic>\u03b1<\/jats:italic> on the investors\u2019 liquidation strategy <jats:italic>X<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> in twelve scenarios. Some interesting properties have been found.<\/jats:p>","DOI":"10.1155\/2021\/8553689","type":"journal-article","created":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T18:21:39Z","timestamp":1630606899000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Liquidation Behaviour Analysis for Stochastic Linear and Nonlinear Systems of Self\u2010Exciting Model with Decay"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1535-2354","authenticated-orcid":false,"given":"Jiangming","family":"Ma","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1773-1240","authenticated-orcid":false,"given":"Xiankang","family":"Luo","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,9,2]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1386-4181(97)00012-8"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.21314\/JOR.2001.041"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/135048602100056"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00531.x"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0219024911006577"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2011.00478.x"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-019-00382-7"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/14697680903373692"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2016.1181274"},{"key":"e_1_2_9_10_2","first-page":"1850059","article-title":"Optimal liquidation under stochastic price impact","volume":"21","author":"Barger W.","year":"2018","journal-title":"International Journal of Theoretical and Applied Finance"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11579-019-00241-1"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12108"},{"key":"e_1_2_9_13_2","unstructured":"VaesJ.andHauserR. Optimal execution strategy with an uncertain volume target 2020 https:\/\/arxiv.org\/pdf\/1810.11454.pdf."},{"key":"e_1_2_9_14_2","unstructured":"EkrenI.andNadtochiyS. Utility-based pricing and hedging of contingent claims in almgren-chriss model with temporary price impact 2020 https:\/\/arxiv.org\/pdf\/1910.01778.pdf."},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11579-015-0148-2"},{"volume-title":"Handbook of Exact Solutions for Ordinary Differential Equations","year":"2003","author":"Andrei D. P.","key":"e_1_2_9_16_2"},{"key":"e_1_2_9_17_2","unstructured":"HorstU.andNaujokatF. Illiquidity and derivative valuation 2018 https:\/\/arxiv.org\/pdf\/0901.0091.pdf."},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2018.2882067"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.10.004"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/8553689.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/8553689.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/8553689","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:50:17Z","timestamp":1723243817000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/8553689"}},"subtitle":[],"editor":[{"given":"Yue","family":"Song","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/8553689"],"URL":"https:\/\/doi.org\/10.1155\/2021\/8553689","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-07-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-08-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-09-02","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"8553689"}}