{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T13:18:39Z","timestamp":1692623919527},"reference-count":20,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["16K13773"],"award-info":[{"award-number":["16K13773"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The paper shows a new weak approximation method for stochastic differential equations as a generalization and an extension of Heath\u2013Platen\u2019s scheme for multidimensional diffusion processes. We reformulate the Heath\u2013Platen estimator from the viewpoint of asymptotic expansion. The proposed scheme is implemented by a Monte Carlo method and its variance is much reduced by the asymptotic expansion which works as a kind of control variate. Numerical examples for the local stochastic volatility model are shown to confirm the efficiency of the method.<\/jats:p>","DOI":"10.1515\/mcma-2019-2044","type":"journal-article","created":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T09:02:14Z","timestamp":1565946134000},"page":"239-252","source":"Crossref","is-referenced-by-count":4,"title":["A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion"],"prefix":"10.1515","volume":"25","author":[{"given":"Yusuke","family":"Okano","sequence":"first","affiliation":[{"name":"Hitotsubashi University , Tokyo Japan (current affiliation: SMBC Nikko Securities Inc., Tokyo, Japan)"}]},{"given":"Toshihiro","family":"Yamada","sequence":"additional","affiliation":[{"name":"Hitotsubashi University , Tokyo , Japan"}]}],"member":"374","published-online":{"date-parts":[[2019,8,16]]},"reference":[{"key":"2023040102122327654_j_mcma-2019-2044_ref_001_w2aab3b7b5b1b6b1ab1b5b1Aa","doi-asserted-by":"crossref","unstructured":"S.  Coskun and R.  Korn,\nPricing barrier options in the Heston model using the Heath\u2013Platen estimator,\nMonte Carlo Methods Appl. 24 (2018), no. 1, 29\u201341.\n10.1515\/mcma-2018-0004","DOI":"10.1515\/mcma-2018-0004"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_002_w2aab3b7b5b1b6b1ab1b5b2Aa","doi-asserted-by":"crossref","unstructured":"P.  Glasserman,\nMonte Carlo Methods in Financial Engineering. Stochastic Modelling and Applied Probability,\nAppl. Math. (New York) 53,\nSpringer, New York, 2004.","DOI":"10.1007\/978-0-387-21617-1"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_003_w2aab3b7b5b1b6b1ab1b5b3Aa","doi-asserted-by":"crossref","unstructured":"E.  Gobet and C.  Labart,\nSharp estimates for the convergence of the density of the Euler scheme in small time,\nElectron. Commun. Probab. 13 (2008), 352\u2013363.\n10.1214\/ECP.v13-1393","DOI":"10.1214\/ECP.v13-1393"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_004_w2aab3b7b5b1b6b1ab1b5b4Aa","doi-asserted-by":"crossref","unstructured":"J.  Guyon,\nEuler scheme and tempered distributions,\nStochastic Process. Appl. 116 (2006), no. 6, 877\u2013904.\n10.1016\/j.spa.2005.11.011","DOI":"10.1016\/j.spa.2005.11.011"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_005_w2aab3b7b5b1b6b1ab1b5b5Aa","doi-asserted-by":"crossref","unstructured":"D.  Heath and E.  Platen,\nA variance reduction technique based on integral representations,\nQuant. Finance 2 (2002), no. 5, 362\u2013369.\n10.1088\/1469-7688\/2\/5\/305","DOI":"10.1088\/1469-7688\/2\/5\/305"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_006_w2aab3b7b5b1b6b1ab1b5b6Aa","unstructured":"P. E.  Kloeden and E.  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I,\nStochastic Analysis (Katata\/Kyoto 1982),\nNorth-Holland Math. Library 32,\nNorth-Holland, Amsterdam (1984), 271\u2013306.","DOI":"10.1016\/S0924-6509(08)70397-0"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_010_w2aab3b7b5b1b6b1ab1b5c10Aa","doi-asserted-by":"crossref","unstructured":"P.  Malliavin,\nStochastic Analysis,\nGrundlehren Math. Wiss. 313,\nSpringer, Berlin, 1997.","DOI":"10.1007\/978-3-642-15074-6"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_011_w2aab3b7b5b1b6b1ab1b5c11Aa","unstructured":"P.  Malliavin and A.  Thalmaier,\nStochastic Calculus of Variations in Mathematical Finance,\nSpringer Finance,\nSpringer, Berlin, 2006."},{"key":"2023040102122327654_j_mcma-2019-2044_ref_012_w2aab3b7b5b1b6b1ab1b5c12Aa","unstructured":"D.  Nualart,\nThe Malliavin Calculus and Related Topics, 2nd ed.,\nSpringer, Berlin, 2006."},{"key":"2023040102122327654_j_mcma-2019-2044_ref_013_w2aab3b7b5b1b6b1ab1b5c13Aa","doi-asserted-by":"crossref","unstructured":"E.  Platen and D.  Heath,\nA Benchmark Approach to Quantitative Finance,\nSpringer Finance,\nSpringer, Berlin, 2006.","DOI":"10.1007\/978-3-540-47856-0"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_014_w2aab3b7b5b1b6b1ab1b5c14Aa","doi-asserted-by":"crossref","unstructured":"A.  Takahashi and T.  Yamada,\nAn asymptotic expansion with push-down of Malliavin weights,\nSIAM J. Financial Math. 3 (2012), no. 1, 95\u2013136.\n10.1137\/100807624","DOI":"10.1137\/100807624"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_015_w2aab3b7b5b1b6b1ab1b5c15Aa","doi-asserted-by":"crossref","unstructured":"A.  Takahashi and T.  Yamada,\nA weak approximation with asymptotic expansion and multidimensional Malliavin weights,\nAnn. Appl. Probab. 26 (2016), no. 2, 818\u2013856.\n10.1214\/15-AAP1105","DOI":"10.1214\/15-AAP1105"},{"key":"2023040102122327654_j_mcma-2019-2044_ref_016_w2aab3b7b5b1b6b1ab1b5c16Aa","doi-asserted-by":"crossref","unstructured":"S.  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Quantif. 7 (2019), no. 1, 143\u2013173.\n10.1137\/17M1142399","DOI":"10.1137\/17M1142399"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/mcma.2019.25.issue-3\/mcma-2019-2044\/mcma-2019-2044.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2019-2044\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2019-2044\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T00:44:22Z","timestamp":1680396262000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2019-2044\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,16]]},"references-count":20,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,8,17]]},"published-print":{"date-parts":[[2019,9,1]]}},"alternative-id":["10.1515\/mcma-2019-2044"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2019-2044","relation":{},"ISSN":["1569-3961","0929-9629"],"issn-type":[{"value":"1569-3961","type":"electronic"},{"value":"0929-9629","type":"print"}],"subject":[],"published":{"date-parts":[[2019,8,16]]}}}