Monotone schemes for fully nonlinear parabolic path dependent PDEs

Jianfeng Zhang () and Jia Zhuo ()
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Jianfeng Zhang: University of Southern California, Department of Mathematics, USA
Jia Zhuo: University of Southern California, Department of Mathematics, USA

Journal of Financial Engineering (JFE), 2014, vol. 01, issue 01, 1-23

Abstract: 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.

Keywords: Monotone scheme; path dependent PDE; viscosity solution; rate of convergence (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (9)

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DOI: 10.1142/S2345768614500056

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