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A Radial Basis Function Partition of Unity Collocation Method for Convection–Diffusion Equations Arising in Financial Applications

Ali Safdari-Vaighani, Alfa Heryudono, Elisabeth Larsson
2014 Journal of Scientific Computing  
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

Ali Safdari-Vaighani
2017 Zenodo  
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

Reza Mollapourasl, Ali Fereshtian, Michèle Vanmaele
2017 Computational Economics  
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

Umberto Soverini, Torsten Söderström
2018 IFAC-PapersOnLine  
[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

Yong-Qing Liu, Rong-Jun Cheng, Hong-Xia Ge
2013 Chinese Physics B  
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

Hakeem Ullah, Saeed Islam, Muhammad Idrees, Mehreen Fiza, Zahoor Ul Haq
2014 International Journal of Differential Equations  
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]

A. Itkin, V. Shcherbakov, A. Veygman
2017 arXiv   pre-print
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

Ali Safdari-Vaighani, Elisabeth Larsson, Alfa Heryudono
2017 Journal of Scientific Computing  
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]

Ali Safdari-Vaighani, Elisabeth Larsson, Alfa Heryudono
2017 arXiv   pre-print
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