Numerical Analysis And Viscosity Solution For The Valuation Of Corporate Value

It is assumed that management selects financing and investment policies with the object of maximizing the value of the firm's outstanding shares and that this is fully anticipated by investors. The basis of the model is the Cox, Ingersoll, Ross (1978) partial differential equations for the value of an asset. This equation is itself the result of combining the Black-Scholes model with the assumption that the pricing function for securities is consistent with rational expectations. The model is used to analyze the financing and investment strategies of a hypothetical firm.In this paper, a numerical solution algorithm by explicit difference schemes is given for the equations. We also show that the explicit difference shemes are stable and convergent and draw graphs of numerical solution of hypothetical firm using Matlab software. By using the viscosity methods, the existence and the uniqueness of the partial differential equation are proved. Then, we compare the numerical solution with viscosity supersolu-tion and viscosity subsolution to give the error estimation.Our main theorem is the comparison theorem and it is used to prove the existence of viscosity solution. The main numerical result is that the difference schemes are stable and convergent.