{"title":"非线性定价期权方程的对称性与精确解","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":"{\"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}","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}
Symmetries and exact solutions of a nonlinear pricing options equation
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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