We introduce a class of Runge-Kutta type schemes for backward stochastic differential equations (BSDEs) in a Markovian framework. The schemes belonging to the class under consideration benefit from a certain stability property. As a consequence, the overall rate of the convergence of these schemes is controlled by their local truncation error. The schemes are categorized by the number of intermediate stages implemented between consecutive partition time instances. The order of the schemes matches the number p of intermediate stages for p≤3. The so-called order barrier occurs at p=3, that is, that it is not possible to construct schemes of order p with p stages, when p>3. The analysis is done under sufficient regularity on the final condition and on the coefficients of the BSDE.
The talk is based on joint work with Dr Jean-François Chassagneux (Imperial College London).