The Application of Proof and Simultaneous Equations in Valuation

The purpose of this chapter is to demonstrate how the notion of “proof” can be used to resolve issues of valuation in finance and how the method of simultaneous equations can be applied to determine the value of shares in two firms that hold an investment of shares in one another at the same time. The reader will be introduced to the notion of proof by arbitrage as it is was first pioneered in modern finance by Modigliani and Miller and then its application in providing guidance to practitioners of valuation will be explored.