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Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) that arise in pricing and hedging of path-dependent derivatives or from use of non-Markovian model, such as rough volatility models in Jacquier and Oumgari, 2019.
Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula
K.-T. Chen · 1957
Earlier work this paper cites.
Integration of paths–a faithful representation of paths by noncommutative formal power series
K.-T. Chen · 1958
Earlier work this paper cites.
Learning long-term dependencies with gradient descent is difficult
Y. Bengio, P. Simard, and P. Frasconi · 1994
Earlier work this paper cites.
Long short-term memory
S. Hochreiter and J. Schmidhuber · 1997
Earlier work this paper cites.
Differential equations driven by rough paths
T. J. Lyons, M. Caruana, and T. Lévy · 2007
Earlier work this paper cites.
A functional extension of the Ito formula
R. Cont and D. Fournie · 2010
Earlier work this paper cites.
Uniqueness for the signature of a path of bounded variation and the reduced path group
B. Hambly and T. Lyons · 2010
Earlier work this paper cites.
A Monte Carlo pricing algorithm for autocallables that allows for stable differentiation
T. Alm, B. Harrach, D. Harrach, and M. Keller · 2013
Earlier work this paper cites.
Functional Itô calculus and stochastic integral representation of martingales
R. Cont and D.-A. Fournié · 2013
Earlier work this paper cites.
Monte Carlo methods in financial engineering
P. Glasserman · 2013
Earlier work this paper cites.
Learning from the past, predicting the statistics for the future, learning an evolving system, 2013
D. Levin, T. Lyons, and H. Ni · 2013
Earlier work this paper cites.
Stochastic calculus and applications
S. N. Cohen and R. J. Elliott · 2015
Earlier work this paper cites.
Stochastic integration by parts and functional Itô calculus
V. Bally, L. Caramellino, R. Cont, F. Utzet, and J. Vives · 2016
Earlier work this paper cites.
A primer on the signature method in machine learning
I. Chevyrev and A. Kormilitzin · 2016
Earlier work this paper cites.
Weak approximation of martingale representations
R. Cont and Y. Lu · 2016
Earlier work this paper cites.
Discretely sampled signals and the rough Hoff process
G. Flint, B. Hambly, and T. Lyons · 2016
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