Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems

Author: 

Reisinger, C
Picarelli, A
Jakobsen, E

Publication Date: 

18 September 2019

Journal: 

Electronic Communications in Probability

Last Updated: 

2020-02-17T12:44:42.513+00:00

Issue: 

2019

Volume: 

24

DOI: 

10.1214/19-ECP256

abstract: 

In N. V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value functions of controlled diffusion processes can be approximated with order 1/6 error by those with controls which are constant on uniform time intervals. In this note we refine the proof and show that the provable rate can be improved to 1/4, which is optimal in our setting. Moreover, we demonstrate the improvements this implies for error estimates derived by similar techniques for approximation schemes, bringing these in line with the best available results from the PDE literature.

Symplectic id: 

1031686

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article