期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Solutions to BSDEs Driven by Both Standard and Fractional Brownian Motions 被引量：5

Solutions to BSDEs Driven by Both Standard and Fractional Brownian Motions
原文传递
导出
摘要 The backward stochastic differential equations driven by both standard and fractional Brownian motions （or, in short, SFBSDE） axe studied. A Wick-It6 stochastic integral for a fractional Brownian motion is adopted. The fractional It6 formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found. The backward stochastic differential equations driven by both standard and fractional Brownian motions （or, in short, SFBSDE） axe studied. A Wick-It6 stochastic integral for a fractional Brownian motion is adopted. The fractional It6 formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found.
作者 Wei-yin FEI Deng-Feng XIA Shu-guang ZHANG
机构地区 Department of Applied Mathematics Department of Statistics and Finance
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第2期329-354,共26页 应用数学学报（英文版）
基金 Supported by National Basic Research Program of China (973 Program, No. 2007CB814901) National Natural Science Foundation of China (No. 71171003) Anhui Natural Science Foundation (No. 090416225) Anhui Natural Science Foundation of Universities (No. KJ2010A037)
关键词 fractional Brownian motion Malliavin calculus fractional It6 formula quasi-conditional expec-tation SFBSDE fractional Brownian motion Malliavin calculus fractional It6 formula quasi-conditional expec-tation SFBSDE
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献34

  • 1Alos, E., Mazet, O., Nualart, D. Stochstic calculus with respect to fractional Brownian motion with Hurst paprameter lesser that 1/2. Stochastic Process. Appl., 86:121-139 (2000).
  • 2Alos, E., Nualart, D. Stochastic integration with respect to the fractional Brownian motion. Stochastics and Stochastics Reports 75:129-152 (2003).
  • 3Bender, C. Explicit solutions of a class of linear fractional BSDEs. Systems & Control Letters, 54:671-680 (2005).
  • 4Biagini, F., Hu, Y., Oksendal, B., Sulem, A. A stochastic maximum principle for processes driven by fractional Brownian motions. Stochastic Process. Appl., 100:233-253 (2002).
  • 5Biagini, F., Oksendal, B. Minimal variance hedging for fractional Brownian motion. Methods and Appli- cations of Analysis 10:347-362 (2003).
  • 6Carmona, P., Coutin, L., Montseny, G. Stochastic integration with respect to fractional Brownian motion. Annales de l'Institut Henri Poincard-Probabilites et Statisques~ 39:27 68 (2003).
  • 7Coutin, L., Qian, Z.M. Stochastic differential equations for fractional Brownian motions. C.R. Acad. Sci. Paris Serie I, 331:75-80 (2000).
  • 8Dai, W., Heyde, C.C. ItS's formula with respect to fractional Brownian motion and its application. J. AppL Math. Stoch. AnaL, 10:439-448 (1996).
  • 9Decreusefond, L., Ustiinel, A.S. Stochastic analysis of the fractional Brownian motion. Potential Anal., 10:177-214 (1999).
  • 10Duncan, T.E., Hu, Y., Pasik-Duncan, B. Stochastic calculus for fractional Brownian motion. I. Theory. SIAM J. Control Optim., 38:582 612 (2000).

同被引文献34

  • 1刘韶跃,杨向群.分数布朗运动环境中标的资产有红利支付的欧式期权定价[J].经济数学,2002(4):35-39. 被引量：32
  • 2刘韶跃,杨向群.分数布朗运动环境中欧式未定权益的定价[J].应用概率统计,2004,20(4):429-434. 被引量：50
  • 3PARDOUX E, PENG S. Adapted solution of a backward stochastic differential equations [J]. Systems control letters, 1990, 14:55-61.
  • 4ROGERS L C G. Arbitrage with fractional Brownian motion [ J ]. Math Finance, 1997,7 : 95-105.
  • 5CARMONA P, COUTIN L, MONTSENY G. Stochastic integration with respect to fractional Brownian motion [J]. Annales de 1' Institut Henri Porncare Probabilities et Statisques, 2003,39 : 27-68.
  • 6DUNCAN T E, HU Y, PASIK-DUNCAN B. Stochastic calculus for fractional Brownian motion [J]. SIAM J Control Optim, 2000,38 : 582-612.
  • 7MISHURA Y S. Stochastic calculus for fractional Brownian motion and related processes [M ]. Berlin Heidelberg:Springer- Verlag, 2008.
  • 8BIAGINI F, HU Y, IKSENDA B, et al. A stochastic maximal principle for processes driven by fractional Brownian motion [J]. Stoch Process Appl, 2002,100: 233-253.
  • 9HU Y, PENG S. Backward stochastic differential equation driven by fractional Brownian motion [J]. SIAM J Control Optim, 2009,48(3) : 1675-1700.
  • 10MATICIUC L, NIE T. Fractional backward stochastic differential equations and fractional backward variational inequalities [J]. J Theoret Probab, 2015,28 ( 1 ) : 337-395.

引证文献5

二级引证文献5

Acta Mathematicae Applicatae Sinica
2013年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部