{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:42:39Z","timestamp":1787323359124,"version":"3.56.0"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100003443","name":"Ministry of Education and Science of the Russian Federation","doi-asserted-by":"publisher","award":["14.A12.31.0007"],"award-info":[{"award-number":["14.A12.31.0007"]}],"id":[{"id":"10.13039\/501100003443","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Finan. Math."],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>We consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him to keep the discretization error small while taking advantage of market trends. Assuming that the portfolio is readjusted at high frequency, we introduce an asymptotic framework in order to derive optimal discretization strategies. More precisely, we formulate the optimization problem in terms of an asymptotic expectation-error criterion. In this setting, the optimal rebalancing times are given by the hitting times of two barriers whose values can be obtained by solving a linear-quadratic optimal control problem. In specific contexts such as in the Black--Scholes model, explicit expressions for the optimal rebalancing times can be derived.<\/jats:p>","DOI":"10.1137\/151004306","type":"journal-article","created":{"date-parts":[[2016,2,18]],"date-time":"2016-02-18T10:02:24Z","timestamp":1455789744000},"page":"34-69","source":"Crossref","is-referenced-by-count":3,"title":["Optimal Discretization of Hedging Strategies with Directional Views"],"prefix":"10.1137","volume":"7","author":[{"given":"Jiatu","family":"Cai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Masaaki","family":"Fukasawa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mathieu","family":"Rosenbaum","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Tankov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,2,18]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-405X(99)00049-5"},{"key":"atypb2","unstructured":"P. Billingsley,\n                      Convergence of Probability Measures\n                      , Wiley Series in Probability and Statistics, Wiley, 2009."},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"M. Fukasawa,\n                      Asymptotically efficient discrete hedging\n                      , Stoch. Anal. Financial Appl. (2011), pp. 331-346.","DOI":"10.1007\/978-3-0348-0097-6_19"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP730"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-013-0215-6"},{"key":"atypb6","first-page":"241","volume":"73","author":"Geiss S.","year":"2002","journal-title":"Stochastics"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.3150\/09-BEJ197"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP959"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013539"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1111\/j.0960-1627.2005.00221.x"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"J. Jacod and A. N. Shiryaev,\n                      Limit Theorems for Stochastic Processes\n                      , Springer-Verlag, Berlin, 2003.","DOI":"10.1007\/978-3-662-05265-5"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1287\/moor.27.1.101.337"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"D. Revuz and M. Yor,\n                      Continuous Martingales and Brownian Motion\n                      , Grundlehren Math. Wiss. 293, Springer, 1999.","DOI":"10.1007\/978-3-662-06400-9"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/090764578"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"H. Rootzen,\n                      Limit distributions for the error in approximations of stochastic integrals\n                      , Ann. Probab. (1980), pp. 241-251.","DOI":"10.1214\/aop\/1176994774"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP940"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"A. Sepp,\n                      When You Hedge Discretely: Optimization of Sharpe Ratio for Delta-Hedging Strategy under Discrete Hedging and Transaction Costs\n                      , SSRN 1865998, Social Science Research Network, 2013; available online from http:\/\/papers.ssrn.com\/sol3\/Papers.cfm?abstract_id=1865998.","DOI":"10.21314\/JOIS.2013.023"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2008.10.002"},{"key":"atypb19","unstructured":"R. Zhang,\n                      Couverture approche\u0301e des options Europe\u0301ennes\n                      , Ph.D. thesis, Ecole des Ponts ParisTech, 1999."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s002450010003"}],"container-title":["SIAM Journal on Financial Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/151004306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:57:07Z","timestamp":1787320627000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/151004306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["10.1137\/151004306"],"URL":"https:\/\/doi.org\/10.1137\/151004306","relation":{},"ISSN":["1945-497X"],"issn-type":[{"value":"1945-497X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1]]}}}