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终端时间可为无限的BSDE解的递归迭代序列的收敛性及解的存在唯一性 被引量：4

The existence and uniqueness for solutions of BSDEs with infinite time horizons and the convergence of recursive iterative sequence for the solutions
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摘要 在某个新的空间上利用压缩映像原理证明了终端时间可为无限的一类多维倒向随机微分方程在该空间上解的存在唯一性,作为推论得到了该类倒向随机微分方程解的递归迭代序列的收敛性. By establishing a strict contraction in a new space,we prove the existence and uniqueness for solutions of a class of multidimensional backward stochastic differential equations with infinite time terminal. As a corollary, we obtain the convergence of the recursive iterative sequence for solutions of backward stochastic differential equations of this type.
作者 侯杰 肖立顺 范胜君
机构地区 中国矿业大学理学院
出处 《云南大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第4期380-384,共5页 Journal of Yunnan University(Natural Sciences Edition)
基金 国家自然科学基金资助项目(11101422) 中央高校基本科研业务费专项资金资助项目(2010LKSX04 JK111729)
关键词 倒向随机微分方程 无穷时间终端 存在唯一性 递归迭代 backward stochastic differential equation infinite time intervals existence and uniqueness re-cursive iteration
分类号 O211.63 [理学—概率论与数理统计]
  • 相关文献

参考文献11

  • 1PARDOUX E, PENG Shi-ge. Adapted solution of a backward stochastic differential equation [ J ]. Systems and Control Letters, 1990,14(1 ) :55-61.
  • 2ELKAROUI N,PENG Shi-ge,QUENEZ M C. Backward stochastic differential equations in finance [ J]. Math Finance, 1997, 7:1-71.
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  • 4朱开永,范胜君,吴祝武.基于g-期望的收敛定理[J].云南大学学报（自然科学版）,2009,31(3):227-231. 被引量：3
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二级参考文献15

  • 1范胜君,朱开永.非线性数学期望的收敛定理[J].中国矿业大学学报,2005,34(3):405-408. 被引量：3
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  • 3PENG Shi-ge. BSDE and related g - expectations [ C ]// Backward stochastic differential equations. El Karoui N, Mazliak L. (ed) , Harlow : Addison Welsey Longman, 1997,141-159.
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  • 6朱红艳.关于g期望的几个经典不等式.云南大学学报：自然科学版,2006,28(2):318-321.
  • 7CHEN Zeng-jing, EPSTEIN L. Ambiguity, risk and asset returns in continuous time [ J ]. Ecomometrica, 2002,70 : 1403- 1443.
  • 8PARDOUX E, PENG Shi-ge. Adapted solution of a backward stochastic differential equation [ J ]. Systems Control Letters, 1990,14:55-61.
  • 9PENG Shi-ge. A general dynamic programming principle and Hamilton -Bellman equation [ J ]. Stochastics, 1992,38 (2) : 119-134.
  • 10El KAROUI N, PENG Shi-ge, QUENCE M C. Backward stochastic differential equation in finance[ J]. Mathematical Finance, 1997,7 ( 1 ) : 1-71.

共引文献6

同被引文献26

  • 1范胜君,张建军.倒向随机微分方程的一个一般的反比较定理(英文)[J].大学数学,2006,22(2):29-35. 被引量：2
  • 2PARDOUX E, PENG S G.Adapted solution of a backward stochastic differential equation [ J ] .Systems Control Letters, 1990, 14: 55-61.
  • 3EL KAROUI N,PENG S G,QUENEZ M C.Backward stochastic differential equations in Finance[ J] .Mathematical Finance, 1997,7:1-71.
  • 4PARDOUX E E.BSDEs, weak convergence and homogenization of semilinear PDEs [ C ].Nonlinear Analysis, Differential Equa- tions and Control.Dordrecht: Kluwer Academic Publishers, 1997 : 503-549.
  • 5PENG S G.Backward stochastic differential equations ,nonlinear expectation and their applications[ C] .Proceedings of the In- ternational Congress of Mathematicians, 2010: 393-432.
  • 6MAO X R. Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients [J].Stochastic Processes and Their Applications, 1995,58 : 281-292.
  • 7HAMADINE S. Multidimensional backward stochastic differential equations with uniformly continuous coefficients [ J ]. Ber- noulli, 2003,9: 517-534.
  • 8FAN S J, JIANG L, DAVISON M.Unlqueness of solutions for multidimensional BSDEs with uniformly continuous generators [J] .C R Acad Sci Paris SOt 1,2010,348:683-686.
  • 9HU Y, TANG S J.Multi-dimensional backward stochastic differential equations of diagonally quadratic generators [ J ]. arXiv: 1408.4579vl [ math.PR] ,2014:1-17.
  • 10BRIAND P, DELYON B, HU Y, et al. Solutions of backward stochastic differential equations [ J ]. Stochastic Processes and Their Applications, 2003,108:109-129.

引证文献4

二级引证文献2

云南大学学报（自然科学版）
2012年 第4期

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