Discrete-time probabilistic approximation of path-dependent stochastic control problems
Abstract
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.
Cite
@article{arxiv.1407.0499,
title = {Discrete-time probabilistic approximation of path-dependent stochastic control problems},
author = {Xiaolu Tan},
journal= {arXiv preprint arXiv:1407.0499},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AAP963 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)