scholarly journals Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I

2016 ◽  
Vol 44 (2) ◽  
pp. 1212-1253 ◽  
Author(s):  
Ibrahim Ekren ◽  
Nizar Touzi ◽  
Jianfeng Zhang
Keyword(s):  
Viscosity Solutions ◽  
Fully Nonlinear ◽  
Nonlinear Parabolic ◽  
Path Dependent

scholarly journals Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II

2016 ◽  
Vol 44 (4) ◽  
pp. 2507-2553 ◽  
Author(s):  
Ibrahim Ekren ◽  
Nizar Touzi ◽  
Jianfeng Zhang
Keyword(s):  
Viscosity Solutions ◽  
Fully Nonlinear ◽  
Nonlinear Parabolic ◽  
Path Dependent

scholarly journals Monotone schemes for fully nonlinear parabolic path dependent PDEs

2014 ◽  
Vol 01 (01) ◽  
pp. 1450005 ◽  
Author(s):  
Jianfeng Zhang ◽  
Jia Zhuo
Keyword(s):  
Rate Of Convergence ◽  
Viscosity Solution ◽  
Fully Nonlinear ◽  
Dependent Case ◽  
Seminal Work ◽  
Monotone Schemes ◽  
Monotone Scheme ◽  
Nonlinear Parabolic ◽  
Path Dependent ◽  
Case Based

In this paper, we extend the results of the seminal work Barles and Souganidis (1991) to path dependent case. Based on the viscosity theory of path dependent PDEs, developed by Ekren et al. (2012a, 2012b, 2014a and 2014b), we show that a monotone scheme converges to the unique viscosity solution of the (fully nonlinear) parabolic path dependent PDE. An example of such monotone scheme is proposed. Moreover, in the case that the solution is smooth enough, we obtain the rate of convergence of our scheme.

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