Error estimates for stochastic differential game: the adverse stopping case

Frédéric Bonnans, Stefania Maroso and Hasnaa Zidani

2006

Publication type:

Paper in peer-reviewed journals

Journal:

IMA Journal of Numerical Analysis, vol. 28, pp. 188-212

DOI:

10.1093/imanum/dri034

HAL:

hal-00979003

Abstract:

We obtain error bounds for monotone approximation schemes of a particular Isaacs equation. This is an extension of the theory for estimating errors for the Hamilton–Jacobi–Bellman equation. To obtain the upper error bound, we consider the ‘Krylov regularization’ of the Isaacs equation to build an approximate sub-solution of the scheme. To get the lower error bound, we extend the method of Barles & Jakobsen(2005, SIAM J. Numer. Anal.) which consists in introducing a switching system whose solutions are local super-solutions of the Isaacs equation.

BibTeX:

@article{Bon-Mar-Zid-2006,
    author={Frédéric Bonnans and Stefania Maroso and Hasnaa Zidani },
    title={Error estimates for stochastic differential game: the adverse 
           stopping case },
    doi={10.1093/imanum/dri034 },
    journal={IMA Journal of Numerical Analysis },
    year={2006 },
    volume={28 },
    pages={188--212},
}