The Annals of Applied Probability

Discrete-time probabilistic approximation of path-dependent stochastic control problems

Xiaolu Tan

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 24, Number 5 (2014), 1803-1834.

Dates
First available in Project Euclid: 26 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1403812362

Digital Object Identifier
doi:10.1214/13-AAP963

Mathematical Reviews number (MathSciNet)
MR3226164

Zentralblatt MATH identifier
1304.65160

Subjects
Primary: 65K99: None of the above, but in this section
Secondary: 93E20: Optimal stochastic control 93E25: Other computational methods

Keywords
Numerical scheme path-dependent stochastic control weak convergence invariance principle

Citation

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


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