Abstract / Description of output
In this paper we undertake the error analysis of the time discretization of systems of Forward-Backward Stochastic Differential Equations (FBSDEs) with drivers having polynomial growth and that are also monotone in the state variable. We show with a counter-example that the natural explicit Euler scheme may diverge, unlike in the canonical Lipschitz driver case. This is due to the lack of a certain stability property of the Euler scheme which is essential to obtain convergence. However, a thorough analysis of the family of θ -schemes reveals that this required stability property can be recovered if the scheme is sufficiently implicit. As a by-product of our analysis we shed some light on higher order approximation schemes for FBSDEs under non-Lipschitz condition. We then return to fully explicit schemes and show that an appropriately tamed version of the explicit Euler scheme enjoys the required stability property and as a consequence converges. In order to establish convergence of the several discretizations we extend the canonical path- and first order variational regularity results to FBSDEs with polynomial growth drivers which are also monotone. These results are of independent interest for the theory of FBSDEs.
Original language | English |
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Pages (from-to) | 2563-2625 |
Number of pages | 63 |
Journal | Annals of Applied Probability |
Volume | 25 |
Issue number | 5 |
Early online date | 3 Jun 2014 |
DOIs | |
Publication status | Published - 2015 |
Keywords / Materials (for Non-textual outputs)
- BSDE
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Lukas Szpruch
- School of Mathematics - Personal Chair of Mathematics of Machine Learning, Programme Director (ATI)
Person: Academic: Research Active