{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T17:18:15Z","timestamp":1785172695094,"version":"3.55.0"},"reference-count":30,"publisher":"Informa UK Limited","issue":"7","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1080\/policies-text-data-mining"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 110-2118-M-008-001-MY2"],"award-info":[{"award-number":["MOST 110-2118-M-008-001-MY2"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST 110-2115-M-152-003"],"award-info":[{"award-number":["MOST 110-2115-M-152-003"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Communications in Statistics - Simulation and Computation"],"published-print":{"date-parts":[[2026,7,3]]},"DOI":"10.1080\/03610918.2025.2474602","type":"journal-article","created":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:54:13Z","timestamp":1742604853000},"page":"2706-2720","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":0,"title":["Pricing formulas for American perpetual knock-out and callable volatility options"],"prefix":"10.1080","volume":"55","author":[{"given":"Hsuan-Ku","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Information Education, National Taipei University of Education","place":["Taiwan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4085-5471","authenticated-orcid":false,"given":"Li-Hsien","family":"Sun","sequence":"additional","affiliation":[{"name":"Graduate Institute of Statistics, National Central University","place":["Taiwan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"301","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1997.tb02749.x"},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.2469\/faj.v45.n4.61"},{"key":"e_1_3_3_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00109-X"},{"key":"e_1_3_3_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12153"},{"key":"e_1_3_3_6_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009814324980"},{"key":"e_1_3_3_7_1","first-page":"270","article-title":"Game variant of a problem on optimal stopping","volume":"10","author":"Dynkin E. B.","year":"1969","unstructured":"Dynkin, E. B. 1969. Game variant of a problem on optimal stopping. Soviet Mathematics\u2013Doklady 10:270\u20134.","journal-title":"Soviet Mathematics\u2013Doklady"},{"key":"e_1_3_3_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-005-0027-3"},{"key":"e_1_3_3_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/105051606000000204"},{"key":"e_1_3_3_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2011.00479.x"},{"key":"e_1_3_3_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/1969318"},{"key":"e_1_3_3_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(87)90026-2"},{"key":"e_1_3_3_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/2327741"},{"key":"e_1_3_3_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2011.00506.x"},{"key":"e_1_3_3_15_1","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12124"},{"key":"e_1_3_3_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4266(95)00034-8"},{"key":"e_1_3_3_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/fut.3990120202"},{"key":"e_1_3_3_18_1","unstructured":"Ishida I. and R. Engle. 2002. Modelling variance of variance: The square root the affine and the CEV GARCH models. NYU working paper."},{"key":"e_1_3_3_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1991.tb00007.x"},{"key":"e_1_3_3_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00107-6"},{"key":"e_1_3_3_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013527"},{"key":"e_1_3_3_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2007.00313.x"},{"key":"e_1_3_3_23_1","unstructured":"Kunita H. and S. Seko. 2004. Game Call Options and Their Exercise Regions Technical Report of the Nanzan Academic Society."},{"key":"e_1_3_3_24_1","doi-asserted-by":"publisher","DOI":"10.1080\/135048698334673"},{"key":"e_1_3_3_25_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-003-0104-5"},{"key":"e_1_3_3_26_1","doi-asserted-by":"publisher","DOI":"10.1137\/130924573"},{"key":"e_1_3_3_27_1","doi-asserted-by":"publisher","DOI":"10.11650\/tjm\/200803"},{"key":"e_1_3_3_28_1","first-page":"32","article-title":"Appendix: A free boundary for the heat equation arising from a problem in mathematical economics","volume":"6","author":"Mckean H. P.","year":"1965","unstructured":"Mckean, H. P. Jr. 1965. Appendix: A free boundary for the heat equation arising from a problem in mathematical economics. Ind. Management Rev 6:32\u20139.","journal-title":"Ind. Management Rev"},{"key":"e_1_3_3_29_1","doi-asserted-by":"publisher","DOI":"10.2307\/3003143"},{"key":"e_1_3_3_30_1","doi-asserted-by":"publisher","DOI":"10.3905\/jod.1993.407868"},{"key":"e_1_3_3_31_1","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12000"}],"container-title":["Communications in Statistics - Simulation and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/03610918.2025.2474602","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.tandfonline.com\/doi\/full-xml\/10.1080\/03610918.2025.2474602","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/03610918.2025.2474602","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T16:34:12Z","timestamp":1785170052000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/03610918.2025.2474602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,21]]},"references-count":30,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,7,3]]}},"alternative-id":["10.1080\/03610918.2025.2474602"],"URL":"https:\/\/doi.org\/10.1080\/03610918.2025.2474602","relation":{},"ISSN":["0361-0918","1532-4141"],"issn-type":[{"value":"0361-0918","type":"print"},{"value":"1532-4141","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,21]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=lssp20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=lssp20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2024-01-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-12-14","order":1,"name":"revised","label":"Revised","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-26","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-21","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}