Yuecai HAN
,
Yifang SUN
. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS[J]. Acta mathematica scientia, Series B, 2018
, 38(2)
: 681
-694
.
DOI: 10.1016/S0252-9602(18)30774-4
[1] Alòs E, Nualart D. Stochastic integration with respect to the fractional brownian motion. Stoch Stoch Rep, 2003, 75(3):129-152
[2] Bender C. Explicit solutions of a class of linear fractional BSDEs. Systems Control Lett, 2005, 54(7):671-680
[3] Bensoussan A. Lectures on Stochastic Control. Lecture Notes in Math. Berlin-New York:Springer, 1982
[4] Biagini F, Hu Y, Øksendal B, Sulem A. A stochastic maximum principle for processes driven by fractional brownian motion. Stochastic Process Appl, 2002, 100:233-253
[5] Bismut J M. Conjugate convex functions in optimal stochastic control. J Math Anal Appl, 1973, 44:384-404
[6] Bismut J M. An introductory approach to duality in optimal stochastic control. SIAM Rev, 1978, 20(1):62-78
[7] Diehl J, Friz P. Backward stochastic differential equations with rough drivers. Ann Probab, 2012, 40(4):1715-1758
[8] Di Nunno G, Øksendal B, Proske F. Malliavin calculus for Lévy processes with applications to finance. Berlin:Springer-Verlag, 2009
[9] Dai W, Heyde C C. Itô formula with respect to fractional brownian motion and its application. J Appl Math Stochastic Anal, 1996, 9(4):439-448
[10] Duncan T, Hu Y, Pasik-Duncan B. Stochasticcalculus for fractional brownian motion I. theory. SIAM J Control Optim, 2000, 38(2):582-612
[11] Fei W, Xia D, Zhang S. Solutions to BSDES driven by both standard and fractional brownian motions. Acta Math Appl Sin Engl Ser, 2013, 29(2):329-354
[12] Han Y, Hu Y, Song J. Maximum principle for general controlled systems driven by fractional brownian motions. Appl Math Optim, 2013, 67(2):279-322
[13] Haussmann U G. General necessary conditions for optimal control of stochastic system. Math Programm Stud, 1976, 6:34-48
[14] Hu Y. Integral transformations and anticipative calculus for fractional brownian motions. Mem Amer Math Soc, 2005, 175(825)
[15] Hu Y, Øksendal B. Fractional white noise calculus and applications to finance. Infin Dimens Anal Quantum Probab Relat Top, 2003, 6(1):1-32
[16] Hu Y, Øksendal B. Partial information linear quadratic control for jump diffusions. SIAM J Control Optim, 2008, 47(4):1744-1761
[17] Hu Y. Peng S. Backward stochastic differential equation driven by fractional brownian motion. SIAM J Control Optim, 2009, 48(3):1675-1700
[18] Hu Y, Zhou X. Stochastic control for linear systems driven by fractional noises. SIAM J Control Optim, 2005, 43(6):2245-2277
[19] Kushner H J. Necessary conditions for continuous parameter stochastic optimization problems. SIAM J Control, 1972, 10:550-565
[20] Lin S. Stochastic analysis of fractional Brownian motions. Stochastics Stochastics Rep, 1995, 55(1):121-140
[21] Nualart D. The Malliavin calculus and related topics. Berlin:Springer, 2006
[22] Nualart D, Rascanu S. Differential equations driven by fractional brownian motion. Collect Math, 2002, 53(1):55-81
[23] Peng S. Backward stochastic differential equation nonlinear expectation and their applications//Proceedings of the International Congress of Mathematicians Hindustan Book Agency. India:New Delhi, 2010:393-432
[24] Peng S. A general stochastic maximum principle for optimal control problems. SIAM J Control Optim, 1990, 28(4):966-979
[25] Pardoux E, Peng S. Adapted solution of a backward stochastic differential equation. Systems Control Lett, 1990, 14(1):55-61
[26] Wu L, Ding Y. Wavelet-based estimator for the Hurst parameters of fractional Brownian sheet. Acta Mathematica Scientia, 2017, 37B(1):205-222
