Numerical solution of variational inequalities: localization with Dirichlet conditions. (Résolution numérique d’inégalités variationnelles: localisation avec conditions de Dirichlet.) (French. English summary) Zbl 1285.60055

Cissé, Mamadou

Afr. Diaspora J. Math. 14, No. 1, 1-23 (2012).

Summary: We present an approximation of viscosity solutions of nonlinear partial differential equations with Dirichlet boundary conditions. Our approach uses a fully nonlinear partial differential equation (PDE) in an unbounded domain. To approximate its unique viscosity solution, one needs to localize the PDE under consideration and to define artificial boundary conditions. It is known that backward stochastic differential equations (BSDEs) are a useful tool to estimate the error due to misspecified Dirichlet boundary conditions on the artificial boundary [D. Lamberton and B. Lapeyre, Introduction au calcul stochastique appliqué à la finance. Paris: Ellipses (1992; Zbl 0898.60002)], but we perfect their approximation of the localization error.

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60J65	Brownian motion
60H30	Applications of stochastic analysis (to PDEs, etc.)
60J55	Local time and additive functionals
60J60	Diffusion processes

Keywords:

forwards backwards stochastic differential equation; variational inequalities; American option; viscosity solutions

Citations:

Zbl 0898.60002

References:

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