{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,13]],"date-time":"2023-08-13T12:28:15Z","timestamp":1691929695009},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"name":"Laboratory of Excellence MME-DII"},{"name":"\u201cRisques Financiers\u201d, Fondation du Risque"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The purpose of this paper is to study the problem of pricing Asian\noptions using the multilevel Monte Carlo method recently introduced by\nGiles [Oper. Res. 56 (2008), no. 3, 607\u2013617] and to prove a central limit theorem of Lindeberg\u2013Feller\ntype for the obtained algorithm.\nIndeed, the implementation of such a method requires first a discretization\nof the integral of the payoff process.\nFor this, we use two well-known second order discretization schemes, namely,\nthe Riemann scheme and the trapezoidal scheme. More precisely, for each of these schemes,\nwe prove a stable law convergence result for the error\non two consecutive levels of the algorithm.\nThis allows us to go further and prove two central limit theorems on the\nmultilevel algorithm providing us a precise description on the choice of the\nassociated parameters with an explicit representation of the limiting variance.\nFor this setting of second order schemes, we give new optimal parameters\nleading to the convergence of the central limit theorem. The complexity of\nthe multilevel Monte Carlo algorithm will be determined.<\/jats:p>","DOI":"10.1515\/mcma-2013-0025","type":"journal-article","created":{"date-parts":[[2014,7,17]],"date-time":"2014-07-17T11:29:06Z","timestamp":1405596546000},"page":"181-194","source":"Crossref","is-referenced-by-count":4,"title":["Multilevel Monte Carlo for Asian options and limit theorems"],"prefix":"10.1515","volume":"20","author":[{"given":"Mohamed","family":"Ben Alaya","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9, LAGA, CNRS (UMR 7539), 99, av. J.B. Cl\u00e9ment, 93430 Villetaneuse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Kebaier","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9, LAGA, CNRS (UMR 7539), 99, av. J.B. Cl\u00e9ment, 93430 Villetaneuse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,7,17]]},"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0025\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0025\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T19:17:58Z","timestamp":1680376678000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0025\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,17]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,5,10]]},"published-print":{"date-parts":[[2014,9,1]]}},"alternative-id":["10.1515\/mcma-2013-0025"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2013-0025","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7,17]]}}}