Weak Estimation of Asset Value Function of Boundary Value Problem Arising in Financial Market
I. U. Amadi *
Department of Mathematics and Statistics, Captain Elechi Amadi Polytechnic, Rumuola, Port Harcourt, Nigeria.
I. Davies
Department of Mathematics, Rivers State University, Nkpolu Oroworokwo, Port Harcourt, Nigeria.
B. O. Osu
Department of Mathematics, Abia State University, Uturu, Abia State, Nigeria.
I. D. Essi
Department of Mathematics, Rivers State University, Nkpolu Oroworokwo, Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper investigated the effectiveness of weak solution on asset value function which is energy estimates on Boundary Value Problem (BVP) of Black-Scholes equation. A set of functions is constructed which transforms the (BVP) Black-Scholes partial differential equation into weak formulations. The analytical solutions: existence, uniqueness, was also obtained in weak form. Therefore, the left hand sides of the energy estimate were constrained and the right hand sides were used as a function of which presents as follows. (i) Increasing the maturity days increases the value of asset. (ii) Increasing volatility of underlying asset also increases the asset value.(iii) there are significant changes in the value of assets (iv) price history of stock market is determined by volatility parameter (v) there is no asset without substantial value. Furthermore, the Table, the surface views with different trajectories, profiles of asset value all were usedand discussed accordingly.
Keywords: Weak solutions, BVP, Sobolev spaces, asset value, stock market