{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T21:14:57Z","timestamp":1791148497413,"version":"4.1.0"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In order to ensure convergence to the viscosity solution, the standard method for discretizing Hamilton\u2013Jacobi\u2013Bellman partial differential equations uses forward\/backward differencing for the drift term. In this paper, we devise a monotone method which uses central weighting as much as possible. In order to solve the discretized algebraic equations, we have to maximize a possibly discontinuous objective function at each node. Nevertheless, convergence of the overall iteration can be guaranteed. Numerical experiments on two examples from the finance literature show higher rates of convergence for this approach compared to the use of forward\/backward differencing only.<\/jats:p>","DOI":"10.1137\/060675186","type":"journal-article","created":{"date-parts":[[2008,4,11]],"date-time":"2008-04-11T18:09:04Z","timestamp":1207937344000},"page":"1580-1601","source":"Crossref","is-referenced-by-count":86,"title":["Maximal Use of Central Differencing for Hamilton\u2013Jacobi\u2013Bellman PDEs in Finance"],"prefix":"10.1137","volume":"46","author":[{"given":"J.","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P. A.","family":"Forsyth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,11]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"787","DOI":"10.57262\/die\/1356060597","volume":"16","author":"Amadori A. L.","year":"2003","journal-title":"Differential Integral Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0893-4983","issn-type":"print"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.1998.013"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1080\/13504869500000005"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"G. Barles,\n                      Convergence of numerical schemes for degenerate parabolic equations arising in finance\n                      , in Numerical Methods in Finance, L. C. G. Rogers and D. 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Working paper, University of Michigan, Ann Arbor, MI, 2005."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/s007800000032"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/8.2.475"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1127483749"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2005.03.009"},{"key":"R15","first-page":"149","volume":"237","author":"Chancellor J. P.","year":"2002","journal-title":"Stochastic Financial Math."},{"key":"R16","unstructured":"S. Chaumont,\n                      A Strong Comparison Result for Viscosity Solutions to Hamilton-Jacobi-Bellman Equations with Dirichlet Conditions on a Non-Smooth Boundary\n                      , Working paper, Institute Elie Cartan, Universit\u00e9 Nancy I, Nancy Cedex, France, 2004."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"P. Forsyth and G. 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