The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 24, Number 5 (2014), 1803-1834.
Discrete-time probabilistic approximation of path-dependent stochastic control problems
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.
Ann. Appl. Probab., Volume 24, Number 5 (2014), 1803-1834.
First available in Project Euclid: 26 June 2014
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Tan, Xiaolu. Discrete-time probabilistic approximation of path-dependent stochastic control problems. Ann. Appl. Probab. 24 (2014), no. 5, 1803--1834. doi:10.1214/13-AAP963. https://projecteuclid.org/euclid.aoap/1403812362