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(Eur J Oper Res 233:184\u2013192, 2014) derive a framework that reduce the coupled Hamilton\u2013Jacobi\u2013Bellman (HJB) equations into a sequence of decoupled HJB equations through introducing a functional operator. The aim of this paper is to develop the iterative finite difference methods (FDMs) with iteration policy to the sequence of decoupled HJB equations derived by Fu et al. (2014). The convergence of the approach is proved and in the proof a number of difficulties are overcome, which are caused by the errors from the iterative FDMs and the policy iterations. Numerical comparisons are made to show that it takes less time to solve the sequence of decoupled HJB equations than the coupled ones.<\/jats:p>","DOI":"10.1007\/s10915-020-01352-4","type":"journal-article","created":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T05:34:33Z","timestamp":1605591273000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Finite Difference Methods for the Hamilton\u2013Jacobi\u2013Bellman Equations Arising in Regime Switching Utility Maximization"],"prefix":"10.1007","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5016-8368","authenticated-orcid":false,"given":"Jingtang","family":"Ma","sequence":"first","affiliation":[]},{"given":"Jianjun","family":"Ma","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,17]]},"reference":[{"key":"1352_CR1","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.1137\/15M1043431","volume":"54","author":"P Azimzadeh","year":"2016","unstructured":"Azimzadeh, P., Forsyth, P.: Weakly chained matrices and impulse control. 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