{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:41:22Z","timestamp":1682494882141},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p>Tankov (2011) improved the Fr\u00e9chet bounds for a bivariate copula when its values on a compact subset of [0, 1]<jats:sup>2<\/jats:sup> are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.<\/jats:p>","DOI":"10.1017\/s0021900200009591","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:44Z","timestamp":1459262984000},"page":"866-875","source":"Crossref","is-referenced-by-count":8,"title":["A Note on \u2018Improved Fr\u00e9chet Bounds and Model-Free Pricing of Multi-Asset Options\u2019 by Tankov (2011)"],"prefix":"10.1017","volume":"49","author":[{"given":"Carole","family":"Bernard","sequence":"first","affiliation":[]},{"given":"Xiao","family":"Jiang","sequence":"additional","affiliation":[]},{"given":"Steven","family":"Vanduffel","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200009591_ref3","doi-asserted-by":"publisher","DOI":"10.2307\/3213097"},{"key":"S0021900200009591_ref1","first-page":"3","volume-title":"Proc. 2011 Actuarial and Financial Mathematics Conf.","year":"2011"},{"key":"S0021900200009591_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994668"},{"key":"S0021900200009591_ref4","volume-title":"An Introduction to Copulas","year":"2006"},{"key":"S0021900200009591_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02056901"},{"key":"S0021900200009591_ref6","volume-title":"Mass Transportation Problems","volume":"II.","year":"1998"},{"key":"S0021900200009591_ref5","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012991221365"},{"key":"S0021900200009591_ref8","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1308662634"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200009591","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:14:05Z","timestamp":1682493245000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200009591\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":8,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S0021900200009591"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200009591","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}