A splitting method for fully nonlinear degenerate parabolic PDEs
Tan, Xiaolu (2013), A splitting method for fully nonlinear degenerate parabolic PDEs, Electronic Journal of Probability, 18, p. n°15. 10.1214/EJP.v18-1967
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01246999
Journal nameElectronic Journal of Probability
Electronic Journal of Probability and Electronic Communications in Probability
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Abstract (EN)Motivated by applications in Asian option pricing, optimal commodity trading etc., we propose a splitting scheme for a fully nonlinear degenerate parabolic PDEs. The splitting scheme generalizes the probabilistic scheme of Fahim, Touzi and Warin to the degenerate case. We also provide a simulation-regression method to make the splitting scheme implementable. General convergence as well as rate of convergence are obtained under reasonable conditions. Finally, we give some numerical tests in an Asian option pricing problem and an optimal hydropower management problem.
Subjects / KeywordsNumerical scheme; nonlinear degenerate PDE; splitting method; viscosity solution
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