{"title":"关于分数阶布朗运动的随机积分","authors":"Joachim Yaakov Nahmani","doi":"10.2139/SSRN.2087921","DOIUrl":null,"url":null,"abstract":"While the Fractional Brownian Motion (FBm) has very interesting properties, such as long range dependency or self-similarity, and is therefore widely exploited in telecommunication or hydrology modeling, it is not applied in mathematical finance because it is not a semi-martingale and violates thus the no arbitrage condition. We nonetheless explain the theory of stochastic integration with FBm as integrators and non stochastic integrands.","PeriodicalId":353809,"journal":{"name":"GeologyRN: Computational Methods in Geology (Topic)","volume":"61 6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":"{\"title\":\"Stochastic Integration with Respect to Fractional Brownian Motion\",\"authors\":\"Joachim Yaakov Nahmani\",\"doi\":\"10.2139/SSRN.2087921\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"While the Fractional Brownian Motion (FBm) has very interesting properties, such as long range dependency or self-similarity, and is therefore widely exploited in telecommunication or hydrology modeling, it is not applied in mathematical finance because it is not a semi-martingale and violates thus the no arbitrage condition. We nonetheless explain the theory of stochastic integration with FBm as integrators and non stochastic integrands.\",\"PeriodicalId\":353809,\"journal\":{\"name\":\"GeologyRN: Computational Methods in Geology (Topic)\",\"volume\":\"61 6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"GeologyRN: Computational Methods in Geology (Topic)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/SSRN.2087921\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"GeologyRN: Computational Methods in Geology (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/SSRN.2087921","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stochastic Integration with Respect to Fractional Brownian Motion
While the Fractional Brownian Motion (FBm) has very interesting properties, such as long range dependency or self-similarity, and is therefore widely exploited in telecommunication or hydrology modeling, it is not applied in mathematical finance because it is not a semi-martingale and violates thus the no arbitrage condition. We nonetheless explain the theory of stochastic integration with FBm as integrators and non stochastic integrands.
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