Corporate Valuation: Analyzing the Theoretical Valuations of Stylized Corporates

Corporations are viewed as perpetual derivatives securities with cash flows defined by deterministic functions of state variables. In time homogeneous and Markovian contexts the valuation of corporate is given by a deterministic function of the state variables. The resulting value function solves an integro-differential equation with a boundary condition of zero at infinity. Solutions are illustrated in dimensions one, two and ten. It is observed that for positive and bounded cash flow functions the value functions cannot be linear. The attitude of a corporate to risk depends on the nonlinearity. In higher dimensions the corporate will typically be a risk taker in some directions and simultaneously a risk avoider in other directions. The valuation theory also leads to new asset pricing equations inferring asset variations from risk neutral covariations. The shift from mean returns and covariances is necessitated by the focus on instantaneous risk exposures represented by measures replacing probabilities.