Article2014

Monotone schemes for fully nonlinear parabolic path dependent PDEs

23 citations0/0 files storedJournal of Financial Engineering

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Stochastic processes and financial applications Advanced Numerical Methods in Computational Mathematics Nonlinear Partial Differential Equations

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.

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References

2005Controlled Markov Processes and Viscosity Solutions 1990Adapted solution of a backward stochastic differential equation 1999Stochastic controls : Hamiltonian systems and HJB equations 2004A numerical scheme for BSDEs 2011Wellposedness of second order backward SDEs 2013Functional Itô calculus and stochastic integral representation of martingales 2014On viscosity solutions of path dependent PDEs 2011A probabilistic numerical method for fully nonlinear parabolic PDEs

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