AASCIT - Journal - All Issues

ISSN: 2375-3927

International Journal of Mathematical Analysis and Applications

The Journal

Manuscript Information

Solution to a Certain Non-Linear Black-Sholes Option Pricing Model Via the Riesz Representation Theorem

International Journal of Mathematical Analysis and Applications
Vol.2 , No. 3, Publication Date: Apr. 25, 2015, Page: 40-46

1614 Views Since April 25, 2015, 1213 Downloads Since Apr. 25, 2015

Paper in PDF (279K)

Follow on

Authors

[1]	Bright O. Osu, Department of mathematics Abia State University, Uturu, Nigeria.
[2]	Chidinma Olunkwa, Department of mathematics Abia State University, Uturu, Nigeria.

Abstract

In this paper, a certain non-linear Black-Scholes equation which incorporates both transaction cost and volatile portfolio risk is obtained. A solution in Sobolev space via the Riesz representation theorem is proffered. Existence of the weak solution is established.

Keywords

Sobolev Space, Non Linear Black-Scholes Equation, Transaction Cost, Portfolio Risk, Riesz Representation Theorem

Reference

[01]	F. Black and M. Scholes .The principle of option and cooperate liabilities. Journal of political economic (1981) 81 637-659
[02]	Black, F., Scholes, M. The valuation of options contracts and test of market efficiency. Journal of Finance (1972) ,27 399–417.
[03]	H.M. Soner, S.E. Shreve, and J. Cvitanic. There is non on trivial hedging portfolio for option pricing with transaction costs
[04]	H. E. Leland. Option pricing and replication with transactions costs. The journal of finance, vol. 40, No.5.(1985), pp.1283-1301
[05]	G. Barles and H. M. Soner.Option pricing with transaction costs and nonlinear Black-Scholes equation. Finance Stochast. 2 (1998),369-397
[06]	P. Amster, C. G. Averbuj, M.C. Mariani and D. Rial. A Black-Scholes option model with transaction costs. Journal of Mathematical Analysis and Applications. 303(2) (2005), 688-695.
[07]	M. Avellaneda, A. Levy and A. Paras. Pricing and Hedging derivative securities in markets and uncertain Volatilities. Applied Mathematical Finance,2(1995),73-88.
[08]	B.O. Osu and C. Olunkwa A solution by stochastic iteration method for nonlinear Black-Scholes equation with transaction cost and volatile portfolio risk in Hilbert space. International Journal of Mathematical Analysis and Application: 1(3) (2014), 43-48.
[09]	B. Mawah. Option pricing with transaction costs and a nonlinear Black-Scholes equation. Department of Mathematics U.U.D.M. Project Report 2007:18. Uppsala University.
[10]	R.A Adam and J.F Fourier. Sobolev spaces Academic Press, 1978.
[11]	M.C. Maraiam, E.K. Ncheuguim and I. Sengupta.Solution to a nonlinear Black-Scholes equation. Electronic Journal of Differential Equations. 158 (2011), 1-10.