Cubature on Wiener space

By Terry Lyons, Nicolas Victoir. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2004

234 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Finance, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8d2257da74b6456ac1d01be08e28f005ffb33b03

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Citations in the corpus

Joint calibration to SPX and VIX options with signature‐based models (2023, background): “Several representations of related quantities in particular for the Brownian case can be found in the literature, see for instance Fawcett (2003), Lyons and Victoir (2004), Lyons and Ni (2015), Boedihardjo et al. (2021), Rossi Ferrucci and Cass (2022).”
On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights (2010, methodology): “For instance, the above methodology is applied in [8] in order to prove convergence of a probabilistic numerical algorithm where the regressions are estimated by using the cubature method of Lyons and Victoir [15] to approximate the distribution of (X,W ).”
The Euler–Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem (2019, background): “, in [12] to deal with weak error estimates for non-smooth functionals and in [3] to deal with hedging errors in the presence of non-smooth pay-offs.”
A regularity structure for rough volatility (2017, methodology): “The Stratonovich formulation opens up the possibility of constructing cubature methods (in the sense of Kusuoka, 2001; Lyons & Victoir, 2004) for rough SV methods.”
General Rough integration, Levy Rough paths and a Levy--Kintchine type formula (2012, methodology): “of) and contains signiﬁ- cant information of the original object, somewhat similar in spirit to Fourier series, and has gained increasing importance in pure and applied mathematics, e.g. [15, 12] and [2, 19]. For instance, in the last reference these ideas were used towards a novel numerical method,”