BSDEs with jumps and path-dependent parabolic integro-differential equations

详细信息    查看全文

• 作者：Falei Wang
• 关键词：Backward stochastic differential equations ; Jump ; diffusion processes ; It么 integral and It么 calculus ; Path ; dependent parabolic integro ; differential equations ; 60H30 ; 60H10 ; 35K10
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：36
• 期：4
• 页码：625-644
• 全文大小：286 KB
• 参考文献：[1]Barles, G., Buckdahn, R. and Pardoux, E., Backward stochastic differential equations and integral-partial differential equations, Stochastics Stochastics Rep., 60, 1997, 57鈥?3.MATH MathSciNet View Article
  [2]Bismut, J. M., Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl., 44, 1973, 384鈥?04.MathSciNet View Article
  [3]Buckdahn, R. and Pardoux E., BSDEs with jumps and associated integro-partial differential equations, preprint.
  [4]Cont, R. and Fourni茅, D. A., Change of variable formulas for non-anticipative functionals on path space, J. Funct. Anal., 259(4), 2010, 1043鈥?072.MATH MathSciNet View Article
  [5]Cont, R. and Fourni茅, D. A., A functional extension of the It么 formula, C. R. Math. Acad. Sci. Paris., 348(1), 2010, 57鈥?1.MATH MathSciNet View Article
  [6]Cont, R. and Fournie, D. A., Functional Ito calculus and stochastic integral representation of martingales, Ann. Probab., 41(1), 2013, 109鈥?33.MATH MathSciNet View Article
  [7]Dupire, B., Functional It么 calculus, Portfolio Research Paper 2009-04, Bloomberg.
  [8]Ekren, I., Keller, C., Touzi, N. and Zhang, J., On viscosity solutions of path dependent PDEs, Ann. Probab., 42(1), 2014, 204鈥?36.MATH MathSciNet View Article
  [9]Ekren, I., Touzi, N. and Zhang, J., Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I. arXiv: 1210.0006
  [10]Ekren, I., Touzi, N. and Zhang, J., Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II. arXiv: 1210.0007
  [11]El Karoui, N., Peng, S. and Quenez, M. C., Backward stochastic differential equation in finance, Math. Finance, 7(1), 1997, 1鈥?1.MATH MathSciNet View Article
  [12]Hu, Y. and Ma, J., Nonlinear Feynman-Kac formula and discrete-functional-type BSDEs with continuous coefficients, Stochastic Process. Appl., 112(1), 2004, 23鈥?1.MATH MathSciNet View Article
  [13]Ma, J. and Yong, J., Forward-backward stochastic differential equations and their applications, Lecture Notes in Mathematics, 1702, Springer-Verlag, Berlin, 1999.
  [14]Ma, J. and Zhang, J., Representation theorems for backward SDEs, Ann. Appl. Probab., 12(4), 2002, 1390鈥?418.MATH MathSciNet View Article
  [15]Ma, J. and Zhang, J., Path regularity for solutions of backward stochastic differential equations, Probab. Theory Related Fields., 122(2), 2002, 163鈥?90.MATH MathSciNet View Article
  [16]Pardoux, E. and Peng, S., Adapted solutions of backward stochastic equations, Systems Control Lett., 14, 1990, 55鈥?1.MATH MathSciNet View Article
  [17]Pardoux, E. and Peng, S., Backward stochastic differential equations and quasilinear parabolic partial differential equations, Stochastic Partial Differential Equations and Their Applications, B. L. Rozuvskii and R. B. Sowers (eds.), Lect. Notes Control Inf. Sci., Vol. 176, Springer-Verlag, Berlin, Heidelberg, New York, 1992, 200鈥?17.MathSciNet View Article
  [18]Peng, S., Probabilistic interpretation for systems of quasilinear parabolic partial differential equation, Stochastics Stochastics Rep., 37, 1991, 61鈥?4.MATH MathSciNet View Article
  [19]Peng, S., A nonlinear Feynman-Kac formula and applications, Control Theory, Stochastic Analysis and Applications (Hangzhou, 1991), World Sci. Publ., River Edge, NJ, 1992, 173鈥?84.
  [20]Peng, S., Note on viscosity solution of path-dependent PDE and G-martingales. arXiv: 1106.1144
  [21]Peng, S. and Wang, F., BSDE, path-dependent PDE and nonlinear Feynman-Kac Formula. arXiv: 1108.4317
  [22]Tang, S. and Li, X., Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim., 32(5), 1994, 1447鈥?475.MATH MathSciNet View Article
  
• 作者单位：Falei Wang (1)
  
  1. Institute for Advanced Research and School of Mathematics, Shandong University, Jinan, 250100, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1860-6261

文摘

This paper deals with backward stochastic differential equations with jumps, whose data (the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.