Cubature on Wiener Space: Pathwise Convergence

Cubature on Wiener Space: Pathwise Convergence Cubature on Wiener space (Lyons and Victoir in Proc. R. Soc. Lond. A 460(2041):169–198, 2004 ) provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpretation of cubature and similar (e.g. the Ninomiya–Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dependent option prices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Cubature on Wiener Space: Pathwise Convergence

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Publisher
Springer-Verlag
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-012-9187-8
Publisher site
See Article on Publisher Site

Abstract

Cubature on Wiener space (Lyons and Victoir in Proc. R. Soc. Lond. A 460(2041):169–198, 2004 ) provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpretation of cubature and similar (e.g. the Ninomiya–Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dependent option prices.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2013

References

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