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A Radial Basis Function Partition of Unity Collocation Method for Convection–Diffusion Equations Arising in Financial Applications
2014
Journal of Scientific Computing
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It is shown that using a node layout that captures the solution features improves the accuracy significantly compared with a uniform node distribution. ...
As an application, RBF-PUM is employed for a two-dimensional American option pricing problem. ...
Combining (2.3), s(x) =ψ(x)u =φ (x)λ =φ (x)A −1 u ⇒ψ(x) =φ A −1 . (2.6) This transformation is valid whenever A is non-singular. ...
doi:10.1007/s10915-014-9935-9
fatcat:uabkavzp6ba3bdlginmtnxo42q
Basket Option Pricing Under Jump Diffusion Models
2017
Zenodo
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Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. ...
For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. ...
Ali Safdari-Vaighani is with the Department of Mathematics, School of Mathematical Sciences and Computer, Allameh Tabataba'i University, Tehran, Iran (e-mail: alisafdari87@gmail.com). ...
doi:10.5281/zenodo.1131169
fatcat:h6lhya4pqvdl7ohzpgfzddmsem
Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility
2017
Computational Economics
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Next, a Crank-Nicolson time discretisation is combined with the operator splitting method to get a fully discrete problem. ...
In this article, we price American options under Heston's stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation ...
We apply a nonuniform discretisation as in in 't Hout and Foulon (2010) , Safdari-Vaighani 2015) , Tavella and Randall (2000) and Haentjens and in 't Hout (2015) . ...
doi:10.1007/s10614-017-9739-8
fatcat:z425oxi4e5dp7dkmte53ngq7oa
Identification of two dimensional complex sinusoids in white noise: a state-space frequency approach
2018
IFAC-PapersOnLine
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[2013-023] Ali Safdari-Vaighani, Alfa Heryudono and Elisabeth Larsson. A
Radial Basis Function Partition of Unity Collocation Method for
Convection-Diffusion Equations. November 2013. ...
Modelling and Analysing a WSN Secure Ag-
gregation Protocol: A Comparison of Languages and Tool Support.
November 2015. ...
doi:10.1016/j.ifacol.2018.09.064
fatcat:gewvslra2bazjnofbwomykpcpi
An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations
2013
Chinese Physics B
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For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. ...
[11] and Golbabai and Safdari-Vaighani used the radial basis function method ...
However, if we do that, it will take a lot of time and a large amount of calculation. ...
doi:10.1088/1674-1056/22/10/100204
fatcat:sndjsuoxlndhrozou4cjjbc35y
An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation
2014
International Journal of Differential Equations
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The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution. ...
[8] used element free Galerkin method (EFG), and Golbabai and Safdari-Vaighani [9] used meshless method using RBF collocation scheme. ...
A 1 , A 2 , A 3 can be divided into two parts: A 1 = L 1 + N 1 , A 2 = L 2 + N 2 , A 3 = L 3 + N 3 . (2) L 1 , L 2 , L 3 contain the linear parts while N 1 , N 2 , N 3 contain the nonlinear parts of the ...
doi:10.1155/2014/106934
fatcat:fl2jke6suvbofonu2gxdnsfboe
Influence of jump-at-default in IR and FX on Quanto CDS prices
[article]
2017
arXiv
pre-print
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We propose a new model for pricing Quanto CDS and risky bonds. ...
A localized version of the RBF partition of unity method is used to solve these 4D PDEs. ...
Victor Shcherbakov also thanks the Department of Finance and Risk Engineering at Tandon School, NYU where he worked on this paper as a visiting scholar. ...
arXiv:1711.07133v1
fatcat:6ng4yk5xizeanb7k4twzw4wqba
Radial Basis Function Methods for the Rosenau Equation and Other Higher Order PDEs
2017
Journal of Scientific Computing
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The error estimates indicate that a high order of convergence can be achieved for the Rosenau equation. The numerical experiments show that both methods perform well. ...
In the two-dimensional case, the Rosenau problem is solved both in a square domain and in an irregular domain with smooth boundary, to illustrate the capability of the RBF-based methods to handle irregular ...
(A.34)For the case n ≥ 2E(t) ≤ a(t) 1 − (n − 1) t 0 k(τ )a n−1 (τ ) dτ 1 n−1 , t ≤ β n , (A.35)
xFig. 13 13 − x j . ...
doi:10.1007/s10915-017-0598-1
fatcat:jugi2m6ya5dqzh2c6miidbf76u
Radial basis function methods for the Rosenau equation and other higher order PDEs
[article]
2017
arXiv
pre-print
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In the two-dimensional case, the Rosenau problem is solved both in a square domain and in a starfish-shaped domain, to illustrate the capability of the RBF-based methods to handle irregular geometries. ...
The error estimates indicate that a high order of convergence can be achieved for the Rosenau equation. The numerical experiments show that both methods perform well. ...
*A.^3)/A; % 1st Derivative matrix D4x = (3*ep^4*(3-24*(ep*dx).^2+8*(ep*dx).^4). ...
arXiv:1705.05737v1
fatcat:qx477n4csraubek7ybffgyerbe