Numerical Analysis and Viscosity Solution for the Valuation of Corporate Value
|Keywords||Black-Scholes formula Brownian motion Difference scheme Stability Convergence Viscosity solution|
The basic assumptions of the model for its value maximization as the goal to determine their fiscal policy and investment policy , which is the only goal of the investors . The model is based Cox, Ingersoll and Ross ( 1978 ) the value of assets evaluation of partial differential equations , the equations in the securities of price and rational expectations assumptions that are consistent , the use of the Black-Scholes model . We use the model to analyze a hypothetical company's financial and investment policies . Shows the differential format given the numerical solution of the equations to prove the stability and convergence of the difference scheme , the numerical solution of a graphical representation , has been calculated on a hypothetical company with Matlab . At the same time , the use of viscosity solution method to prove the existence of the model involves nonlinear partial differential equations , uniqueness and properties of the solution and as a basis to construct upper and lower solutions of this equation , numerical analysis solutions were compared , the error estimate is given . Theoretically proved that the comparison principle under certain assumptions , and as a basis to prove a viscous solution is unique there . The main numerical results , the model is stable difference scheme, and the numerical solution converges to the solution of the original problem .