{"title":"Symmetries and exact solutions of a nonlinear pricing options equation","authors":"M. Dyshaev, V. Fedorov","doi":"10.13108/2017-9-1-29","DOIUrl":null,"url":null,"abstract":"We study the group structure of the Schönbucher–Wilmott equation with a free parameter, which models the pricing options. We find a five-dimensional group of equivalence transformations for this equation. By means of this group we find four-dimensional Lie algebras of the admitted operators of the equation in the cases of two cases of the free term and we find a three-dimensional Lie algebra for other nonequivalent specifications. For each algebra we find optimal systems of subalgebras and the corresponding invariant solutions or invariant submodels.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"17 1","pages":"29-40"},"PeriodicalIF":0.5000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ufa Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13108/2017-9-1-29","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
We study the group structure of the Schönbucher–Wilmott equation with a free parameter, which models the pricing options. We find a five-dimensional group of equivalence transformations for this equation. By means of this group we find four-dimensional Lie algebras of the admitted operators of the equation in the cases of two cases of the free term and we find a three-dimensional Lie algebra for other nonequivalent specifications. For each algebra we find optimal systems of subalgebras and the corresponding invariant solutions or invariant submodels.
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