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Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment

Rafael Company, Lucas Jódar, Enrique Ponsoda (2008)

Banach Center Publications

This paper deals with the construction of numerical solution of the Black-Scholes (B-S) type equation modeling option pricing with variable yield discrete dividend payment at time t d . Firstly the shifted delta generalized function δ ( t - t d ) appearing in the B-S equation is approximated by an appropriate sequence of nice ordinary functions. Then a semidiscretization technique applied on the underlying asset is used to construct a numerical solution. The limit of this numerical solution is independent of the...

Numerical solution of parabolic equations in high dimensions

Tobias Von Petersdorff, Christoph Schwab (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the numerical solution of diffusion problems in ( 0 , T ) × Ω for Ω d and for T > 0 in dimension d 1 . We use a wavelet based sparse grid space discretization with mesh-width h and order p 1 , and h p discontinuous Galerkin time-discretization of order r = O ( log h ) on a geometric sequence of O ( log h ) many time steps. The linear systems in each time step are solved iteratively by O ( log h ) GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an L 2 ( Ω ) -error of O ( N - p ) for u ( x , T ) where N is the total number of operations,...

Numerical solution of parabolic equations in high dimensions

Tobias von Petersdorff, Christoph Schwab (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the numerical solution of diffusion problems in (0,T) x Ω for Ω d and for T > 0 in dimension dd ≥ 1. We use a wavelet based sparse grid space discretization with mesh-width h and order pd ≥ 1, and hp discontinuous Galerkin time-discretization of order r = O ( log h ) on a geometric sequence of O ( log h ) many time steps. The linear systems in each time step are solved iteratively by O ( log h ) GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an L2(Ω)-error of O(N-p) for u(x,T)...

Numerical study of the stopping of aura during migraine

C. Pocci, A. Moussa, F. Hubert, G. Chapuisat (2010)

ESAIM: Proceedings

This work is devoted to the study of migraine with aura in the human brain. Following [6], we class migraine as a propagation of a wave of depolarization through the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly presented. The equation is considered in a duct containing a bend, in order to model one of the numerous circumvolutions of the brain. For a wide set of parameters, one can establish the existence...

Numerical study on the blow-up rate to a quasilinear parabolic equation

Anada, Koichi, Ishiwata, Tetsuya, Ushijima, Takeo (2017)

Proceedings of Equadiff 14

In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation u t = u 2 ( u x x + u ) . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].

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