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1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin Ann. Appl. Probab. 214 : 1322-1364 2011 for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent or non-Markovian case for a general stochastic control problem. General convergence result is obtained by weak convergence method in spirit of Kushner and Dupuis 19. We also get a rate of convergence using the invariance principle technique as in Dolinsky 7, which is better than that obtained by viscosity solution method. Finally, by approximating the conditional expectations arising in the numerical scheme with simulation-regression method, we obtain an implementable scheme.

Keywords : path-dependent stochastic control weak conver-gence Numerical scheme invariance principle MSC 2010 Primary 65K99 secondary 93E20 93E25

Author: Xiaolu Tan -

Source: https://hal.archives-ouvertes.fr/


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