Related papers: Full grid solution for multi-asset options pricing…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…
We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of…
This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…
In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…
The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation between the spatial variable and the parameter. In this…
Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…
Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.…
Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultrafast numerical solutions of high-dimensional…
In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework…
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…
We study penalization coupled with time discretization for decoupled Markovian doubly reflected BSDEs with obstacles \(p_b(t,X_t)\le Y_t\le p_w(t,X_t)\). The DRBSDE is approximated by a penalized BSDE with parameter \(\lambda\) and…