Understand
Market events such as order placement and order cancellation are examples of the complex and substantial flow of data that surrounds a modern financial engineer.
- New mathematical techniques, developed to describe the interactions of complex oscillatory systems (known as the theory of rough paths) provides new tools for analysing and describing these data streams and extracting the vital information.
- In this paper we illustrate how a very small number of coefficients obtained from the signature of financial data can be sufficient to classify this data for subtle underlying features and make useful predictions.
- This paper presents financial examples in which we learn from data and then proceed to classify fresh streams.
Built on
Kuo-Tsai Chen, Integration of paths, geometric invariant and generalized Campbell-Baker-Hausdorff formula , Ann. Math. 65
1957
Earlier work this paper cites.
Terry Lyons, Differential equations driven by rough signal , Revista Matematica Iberoamericana 14
1998
Earlier work this paper cites.
E. Peter Kloeden and Eckhard Platen, Numerical Solution of Stochastic Differential Equations , Springer-Verlag Berlin Heidelberg New York, 1999
1999
Earlier work this paper cites.
Terry Lyons and Zhongmin Qian, System Control and Rough Paths , Oxford Mathematical Monographs, Clarendon Press, 2002
2002
Earlier work this paper cites.
Shigeo Kusuoka, Approximation of expectation of diffusion process based on Lie algebra and Malliavin calculus , Adv. Math. Econ. 6
2004
Earlier work this paper cites.
Similar
Terry Lyons and Nicolas Victoir, Cubature on Wiener Space , Proc. R. Soc. Lond. A 460
2004
Cited alongside, same era.
Terry Lyons, Michael Caruana, and Thierry Lévy, Differential Equations Driven by Rough Paths , Ecole d’Eté de Porbabilités de Saint-Flour XXXIV - 2004, Lecture Notes in Mathematics, Springer, 2007
2007
Cited alongside, same era.
Lajos Gergely Gyurkó, Numerical Methods for Approximating Solutions to Rough Differential Equations , DPhil Thesis, University of Oxford, 2009
2009
Cited alongside, same era.
Peter Friz and Nicolas Victoir, Multidimensional Stochastic Processes as Rough Path , Cambridge University Press, 2010
2010
Cited alongside, same era.
Then
Lajos Gergely Gyurkó and Terry Lyons, Rough Paths based Numerical Algorithms in Computational Finance , Mathematics in Finance (Santiago Carrillo Menéndez and José Luis Fernández Pérez, eds.), American Mathematical Society, Real Sociedad Matemática Española, 2010, pp. 397–405
2010
Later among the works it cites.
Ben Hambly and Terry Lyons, Uniqueness for the signature of a path of bounded variation and the reduced path group , Annals of Mathematics 171
2010
Later among the works it cites.
Peter Bühlmann and Sara van der Geer, Statistics for High-Dimensional Data: Methods, Theory and Applications , Springer Series in Statistics, Springer, 2011
2011
Later among the works it cites.
Terry Lyons, Hao Ni, and Daniel Levin, Learning from the past, predicting the statistics of the future, learning an evolving system , Preprint, 2013
2013
Closest in time.
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