Discrete-time probabilistic approximation of path-dependent stochastic control problems
Tan, Xiaolu (2014), Discrete-time probabilistic approximation of path-dependent stochastic control problems, The Annals of Applied Probability, 24, 5, p. 1803-1834. http://dx.doi.org/10.1214/13-AAP963
TypeArticle accepté pour publication ou publié
Journal nameThe Annals of Applied Probability
Institute of Mathematical Statistics
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Abstract (EN)We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322–1364] for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or non-Markovian) case for a general stochastic control problem. A general convergence result is obtained by a weak convergence method in the spirit of Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in Continuous Time (1992) Springer]. We also get a rate of convergence using the invariance principle technique as in Dolinsky [Electron. J. Probab. 17 (2012) 1–5], 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.
Subjects / Keywordsinvariance principle; weak convergence; path-dependent stochastic control; Numerical scheme
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