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Computational and Applied Mathematics Journal

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Numerical Solution of Stochastic Model with Risk Measures via Finite Element Method

Computational and Applied Mathematics Journal
Vol.3 , No. 2, Publication Date: Jul. 5, 2017, Page: 6-12

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Authors

[1]	Chidinma Olunkwa, Department of Mathematics, Abia State University, Uturu, Nigeria.
[2]	Bright O. Osu, Department Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
[3]	Anthony C. Akpanta, Department of Statistics, Abia State University, Uturu, Nigeria.
[4]	F. Nwite Chuku, Department of Mathematics, Abia State University, Uturu, Nigeria.

Abstract

In this paper we investigate the use of finite element method (FEM) as a numerical solution of the partial differential equations arising in finance. First the Black-Scholes equation with transaction cost measure and Portfolio risk measure is established. The FEM is then used to transform the differential equation into an algebraic system of equations and to discretize the continuous domain of the problem by means series of simple geometric forms called finite elements, for which the governing relations on the entire continuous domain are valid on each element. Under some assumptions, the approximate solution in the entire continuous domain of the problem is obtained by means of trial function also called the form functions.

Keywords

Black-Scholes Equation, Finite Element Method, Transaction Cost Measure, Portfolio Risk Measure

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