A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation ...

This work focuses on radial basis functions containing no parameters with the main objective being to comparatively explore more of their effectiveness. For this, a total sixteen forms shapeless are gathered and investigated under context pattern recognition problem through structure function neural networks, use Representational Capability (RC) algorithm. Different sizes datasets disturbed noi...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. Thus, the number of nodes in the stencils can be relatively large compared to the resulting accuracy. The generalization of mehrstellenverfahren (compact) FD (CFD) formu...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. The generalization of compact FD formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil ...

The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation method with global basis functions. It is known to have exponentional convergence for interpolation problems. We descretize nonlinear elliptic PDEs by the MQ method. This results in modest size systems of nonlinear algebraic equations which can be eeciently continued by standard continuation software such as auto and c...

The total variation (TV) denoising method is a PDE-based technique that preserves the edges well but has undesirable staircase effect in some cases, namely, the translation of smooth regions (ramps) into piecewise constant regions (stairs). This paper introduces a novel mesh-free approach using TV (ROFmodel) regularization and radial basis function (RBF) for the numerical approximation of TV-ba...