JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (07): 63-68.doi: 10.6040/j.issn.1671-9352.0.2014.041

Previous Articles     Next Articles

Backward stochastic Volterra integral equations with general martingales

ZHAO Jie1,3, SHI Yu-feng2,3   

  1. 1. The People's Bank of China Heze Central Subbranch, Heze 274000, Shandong, China;
    2. Institute for Financial Studies, Shandong University, Jinan 250100, Shandong, China;
    3. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received:2014-02-03 Online:2014-07-20 Published:2014-09-15

PDF (PC)

1129

Abstract: The existence and uniqueness result of the adapted M-solution of backward stochastic Volterra integral equations (BSVIEs) driven by general martingales under Lipschitz conditions was proved, and the duality principles of the linear BSVIEs driven by general martingales were given. At last a comparison theorem of this kind of BSVIEs was showed by virtue of the duality principles.

Key words: adapted M-solution, Backward stochastic Volterra integral equation, duality principle

CLC Number: 

  • O211.6
[1] PARDOUX E, PENG Shige. Adapted solution of a backward stochastic equation[J]. Systems & Control Letters, 1990, 14(1):55-61.
[2] EL KAROUI N, HUANG S. A general result of existence and uniqueness of backward stochastic differential equations[C]// Pitman Research Notes in Mathematics Series. Harlow: Longman Higher Education, 1997, 364(1):27-36.
[3] 李娟. 由一般鞅驱动的倒向随机微分方程[J]. 山东大学学报:理学版,2005,40(4):70-76.
LI Juan. Backward stochastic differential equations with general martingale[J]. Journal of Shandong University:Natural Science, 2005, 40(4):70-76.
[4] YONG Jiongmin. Backward stochastic Volterra integral equations and some related problems[J]. Stochastic Processes and their Applications, 2006, 116(5):779-795.
[5] YONG Jiongmin. Well-posedness and regularity of backward stochastic Volterra integral equation[J]. Probability Theory & Related Fields, 2008, 142(1-2):1-77.
[6] SHI Yufeng, WANG Tianxiao. Solvability of general backward stochastic Volterra integral equations with non-Lipschitz conditions[J]. J Korean Math Soc, 2012, 49(6):1301-1321.
[7] YONG Jiongmin. A deterministic linear quadratic time-inconsistent optimal control problem[J]. Mathematical Control & Related Fields, 2011, 1:83-118.
[8] YONG Jiongmin. Time-inconsistent optimal control problem and the equilibrium HJB equation[J]. Mathematical Control & Related Fields, 2012, 2:271-329.
[9] WANG Tianxiao, SHI Yufeng. A class of time inconsistent risk measures and backward stochastic Volterra integral equations[J]. Risk and Decision Analysis, 2013, 4:17-24.
[10] DUFFIE D, EPSTEIN L. Stochastic differential utility[J]. Econometrica, 1992, 60:353-394.
[11] 严加安. 鞅与随机积分引论[M]. 上海:上海科学技术出版社,1981:212-214.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd