RUNGE-KUTTA SCHEMES FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

By Jean-François Chassagneux, D. Crisan. 2014

66 citations recorded by the source corpus.

We study the convergence of 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. We show that the order of the schemes matches the number $p$ of intermediate stages for $p\le3$. Moreover, we show that 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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/17adccfb00ec116d4a285f9d01a07d40a5bf8baf

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Citations in the corpus

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2017, unknown): “…deterministic approximation methods for PDEs, to Bally and Pagès (2003), Bender and Denk (2007), Bender et al. (2017), Bouchard and Touzi (2004), Chassagneux (2014), Chassagneux and Crisan (2014), Chassagneux and Richou (2015, 2016), Crisan and Manolarakis (2010, 2012, 2014), Crisan et al.…”
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks (2019, methodology): “, [2, 6, 7, 10, 12, 13, 17, 18, 19, 20, 25, 26, 27, 28, 38, 39, 31, 32, 40, 41, 42, 43, 44, 45, 46, 57, 69, 70, 71, 72, 73, 74, 78, 79, 82, 83, 84, 85, 89, 90, 91, 96, 102, 103, 104] for probabilistic approximation methods for PDEs using discretizations of the associated backward stochastic differen”
Numerical simulation of quadratic BSDEs (2013, unknown): “5, that is to say the minimal rate proved in this paper, and 1 the general optimal rate for the Euler scheme; see, for example, [11, 22].”