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We investigate the approximation of path functionals.
Functions of positive and negative type, and their connection with the theory of integral equations
J. Mercer · 1909
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Über lineare Methoden in der Wahrscheinlichkeitsrechnung
K. Karhunen · 1947
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Fonctions aléatoires du second ordre
M. Loève · 1948
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G. Szegö · 1975
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The valuation of warrants: Implementing a new approach
E. S. Schwartz · 1977
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Analysis of approximation methods for differential and integral equations
H. J. Reinhardt · 1985
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Non-Uniform Random Variate Generation
L. Devroye · 1986
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Stochastic Finite Elements: A Spectral Approach
R. Ghanem and P. Spanos · 1991
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Sample quantiles in statistical packages
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A Comparison of Some Monte Carlo and Quasi Monte Carlo Techniques for Option Pricing
P. A. Acworth, M. Broadie, and P. Glasserman · 1998
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Option valuation using the fast fourier transform
P. Carr and D. Madan · 1999
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Functional quantization for numerics with an application to option pricing
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Differential Equations Driven by Rough Paths
T. J. Lyons, M. Caruana, and T. Lévy · 2007
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Uniqueness for the signature of a path of bounded variation and the reduced path group
B. Hambly and T. Lyons · 2010
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On the expected uniform error of geometric brownian motion approximated by the lévy-ciesielski construction, 2017
B. Brown, M. Griebel, F. Y. Kuo, and I. H. Sloan · 2017
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Reconstruction for the signature of a rough path
X. Geng · 2017
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Numerical method for model-free pricing of exotic derivatives using rough path signatures
T. J. Lyons, S. Nejad, and I. P. Arribas · 2019
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Sig-SDEs model for quantitative finance, 2020
I. P. Arribas, C. Salvi, and L. Szpruch · 2020
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An optimal polynomial approximation of brownian motion
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Hilbert space methods for reduced-rank gaussian process regression
A. Solin and S. Särkkä · 2020
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On a Chen-Fliess approximation for diffusion functionals
C. Litterer and H. Oberhauser · 2014
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Temporal correlations of the running maximum of a brownian trajectory
O. Bénichou, P. L. Krapivsky, C. Mejía-Monasterio, and G. Oshanin · 2016
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Deep learning for exotic option valuation
J. Cao, J. Chen, J. C. Hull, and Z. Poulos · 2021
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