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    Fu, Yu Zhao, Weidong and Zhou, Tao 2017. Efficient spectral sparse grid approximations for solving multi-dimensional forward backward SDEs. Discrete and Continuous Dynamical Systems - Series B, Vol. 22, Issue. 9, p. 3439.
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Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

  • Tao Kong (a1), Weidong Zhao (a1) and Tao Zhou (a2)
Abstract

In this paper, we are concerned with probabilistic high order numerical schemes for Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic PDEs, it is shown by Cheridito, Soner, Touzi and Victoir [4] that the associated exact solutions admit probabilistic interpretations, i.e., the solution of a fully nonlinear parabolic PDE solves a corresponding second order forward backward stochastic differential equation (2FBSDEs). Our numerical schemes rely on solving those 2FBSDEs, by extending our previous results [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751.]. Moreover, in our numerical schemes, one has the flexibility to choose the associated forward SDE, and a suitable choice can significantly reduce the computational complexity. Various numerical examples including the HJB equations are presented to show the effectiveness and accuracy of the proposed numerical schemes.

Copyright
COPYRIGHT: © Global-Science Press 2015 
Corresponding author
*Corresponding author. Email addresses: vision.kt@gmail.com (T. Kong), wdzhao@sdu.edu.cn (W. Zhao), tzhou@lsec.cc.ac.cn (T. Zhou)
References
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
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