{"title":"重新审视CEV模型","authors":"Wen Cheng, Tianyou Zhang","doi":"10.2139/ssrn.2487669","DOIUrl":null,"url":null,"abstract":"This note introduces a mathematically rigorous short time approximation of the transition density function of the CEV model. We first apply a change of variable to the CEV operator and transform it to a Schrodinger operator with an inverse square potential, and then construct a Neumann series to the new opeator under weighted Sobolev spaces. To the author’s knowledge, this is the first time that a mathematically rigorous construction for the CEV model is obtained in the financial mathematics literature.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The CEV Model Revisited\",\"authors\":\"Wen Cheng, Tianyou Zhang\",\"doi\":\"10.2139/ssrn.2487669\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This note introduces a mathematically rigorous short time approximation of the transition density function of the CEV model. We first apply a change of variable to the CEV operator and transform it to a Schrodinger operator with an inverse square potential, and then construct a Neumann series to the new opeator under weighted Sobolev spaces. To the author’s knowledge, this is the first time that a mathematically rigorous construction for the CEV model is obtained in the financial mathematics literature.\",\"PeriodicalId\":177064,\"journal\":{\"name\":\"ERN: Other Econometric Modeling: Derivatives (Topic)\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ERN: Other Econometric Modeling: Derivatives (Topic)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.2487669\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERN: Other Econometric Modeling: Derivatives (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.2487669","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This note introduces a mathematically rigorous short time approximation of the transition density function of the CEV model. We first apply a change of variable to the CEV operator and transform it to a Schrodinger operator with an inverse square potential, and then construct a Neumann series to the new opeator under weighted Sobolev spaces. To the author’s knowledge, this is the first time that a mathematically rigorous construction for the CEV model is obtained in the financial mathematics literature.
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