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Vol.1 , No. 3, Publication Date: Aug. 12, 2014, Page: 43-48
 and then propose an explicit steepest decent type stochastic method for the approximate solution of the LCP govern by a maximal monotone operator in Hilbert space. This scheme is shown to converge strongly to the non-zero solution of the LCP.&picture=http://www.aascit.org/aascit/decorators/img/journal/921.jpg)
| [1] | Bright O. Osu, Department of Mathematics, Abia State University, Uturu, Nigeria. |
| [2] | Chidinma Olunkwa, Department of Mathematics Abia State University, Uturu, Nigeria. |
We introduce a stochastic iteration method for the solution of a non-linear Black- Scholes equation which incorporates both the transaction cost and volatile portfolio risk measures. We first reduce the equation to a linear complementarity problem (LCP) and then propose an explicit steepest decent type stochastic method for the approximate solution of the LCP govern by a maximal monotone operator in Hilbert space. This scheme is shown to converge strongly to the non-zero solution of the LCP.
Keywords
BS Non-Linear Equation, Transaction Cost Measure, Volatile Portfolio Risk Measure, LCP, Hilbert Space
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