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An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented.
“Valuing American options by simulation: a simple least-squares approach”
Francis Longstaff and Eduardo Schwartz · 2001
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“Monte Carlo valuation of American options”
L… Rogers · 2002
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“Efficient Classical Simulation of Slightly Entangled Quantum Computations”
Guifré Vidal · 2003
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“Primal-dual simulation algorithm for pricing multidimensional American options”
Leif Andersen and Mark Broadie · 2004
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“Computational methods for option pricing”
Yves Achdou and Olivier Pironneau · 2005
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“Why are high-dimensional finance problems often of low effective dimension?”
Xiaoqun Wang and Ian Sloan · 2005
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“Conjugate Gradient Methods”
Jorge Nocedal and Stephen. Wright · 2006
Earlier work this paper cites.
“Optimization Algorithms on Matrix Manifolds”
P.-A. Absil, R. Mahony and R. Sepulchre · 2008
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“A New Scheme for the Tensor Representation”
Wolfgang Hackbusch and Stefan Kühn · 2009
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“Breaking the curse of dimensionality, or how to use SVD in many dimensions”
I.. Oseledets and E.. Tyrtyshnikov · 2009
Earlier work this paper cites.
“TT-cross approximation for multidimensional arrays”
Ivan. Oseledets and Eugene Tyrtyshnikov · 2010
Earlier work this paper cites.
“On manifolds of tensors of fixed TT-rank”
Sebastian Holtz, Thorsten Rohwedder and Reinhold Schneider · 2011
Earlier work this paper cites.
“Tensor-Train Decomposition”
I. Oseledets · 2011
Earlier work this paper cites.
“Tensor Spaces and Numerical Tensor Calculus”
Wolfgang Hackbusch · 2012
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“The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format”
S. Holtz, T. Rohwedder and R. Schneider · 2012
Earlier work this paper cites.
“On manifolds of tensors of fixed TT-rank”
Sebastian Holtz, Thorsten Rohwedder and Reinhold Schneider · 2012
Earlier work this paper cites.
“The alternating linear scheme for tensor optimization in the tensor train format”
Sebastian Holtz, Thorsten Rohwedder and Reinhold Schneider · 2012
Cited alongside, same era.
“mlOSP: Towards a Unified Implementation of Regression Monte Carlo Algorithms”, 2020
Mike Ludkovski · 2012
Cited alongside, same era.
“Monte Carlo methods in financial engineering”
Paul Glasserman · 2013
Cited alongside, same era.
“Constructive representation of functions in low-rank tensor formats”
Ivan Oseledets · 2013
Cited alongside, same era.
“Tensor spaces and hierarchical tensor representations”
Wolfgang Hackbusch and Reinhold Schneider · 2014
Cited alongside, same era.
“Low-rank tensor completion by Riemannian optimization”
Daniel Kressner, Michael Steinlechner and Bart Vandereycken · 2014
“Advanced Simulation-Based Methods for Optimal Stopping and Control: With Applications in Finance”
Denis Belomestny and John Schoenmakers · 2018
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“Chebyshev interpolation for parametric option pricing”
Maximilian Gaß, Kathrin Glau, Mirco Mahlstedt and Maximilian Mair · 2018
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“Dual Pricing of American Options by Wiener Chaos Expansion”
Jérôme Lelong · 2018
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“Deep optimal stopping”
Sebastian Becker, Patrick Cheridito and Arnulf Jentzen · 2019
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“Tensor decompositions for high-dimensional Hamilton-Jacobi-Bellman equations”
Sergey Dolgov, Dante Kalise and Karl Kunisch · 2019
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“Variational Monte Carlo – bridging concepts of machine learning and high-dimensional partial differential equations”
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Cited alongside, same era.
“Adaptive low-rank methods: Problems on Sobolev spaces”
Markus Bachmayr and Wolfgang Dahmen · 2016
Cited alongside, same era.
“Pricing under rough volatility”
Christian Bayer, Peter Friz and Jim Gatheral · 2016
Cited alongside, same era.
“Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations”
Markus Bachmayr, Reinhold Schneider and André Uschmajew · 2016
Cited alongside, same era.
“Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure”
Michael Steinlechner · 2016
Cited alongside, same era.
“Parametric PDEs: sparse or low-rank approximations?”
Markus Bachmayr, Albert Cohen and Wolfgang Dahmen · 2017
Cited alongside, same era.
“Adaptive stochastic Galerkin FEM with hierarchical tensor representations”
Martin Eigel, Max Pfeffer and Reinhold Schneider · 2017
Cited alongside, same era.
Martin Eigel, Reinhold Schneider, Philipp Trunschke and Sebastian Wolf · 2019
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“Stable ALS approximation in the TT-format for rank-adaptive tensor completion”
Lars Grasedyck and Sebastian Krämer · 2019
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Jérôme Lelong · 2019
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“Approximating the Stationary Hamilton-Jacobi-Bellman Equation by Hierarchical Tensor Products”
Mathias Oster, Leon Sallandt and Reinhold Schneider · 2019
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“Low rank tensor decompositions for high dimensional data approximation, recovery and prediction”
Alexander Wolf · 2019
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“Pricing American options by exercise rate optimization”
Christian Bayer, Raúl Tempone and Sören Wolfers · 2020
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“Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations”
Martin Eigel, Manuel Marschall, Max Pfeffer and Reinhold Schneider · 2020
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Konstantin Fackeldey, Mathias Oster, Leon Sallandt and Reinhold Schneider · 2020
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“Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing”
Kathrin Glau, Daniel Kressner and Francesco Statti · 2020
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“Geometric methods on low-rank matrix and tensor manifolds”
A. Uschmajew and B. Vandereycken · 2020
Later among the works it cites.