Mathematical Analysis and Stochastic Extension of the Miller-Modigliani Theory

摘要

This paper deals with the problem of the financial valuation of a firm and its shares of stock with general financing policies in a partial equilibrium framework. The model assumes a time-dependent discount rate and a general stochastic environment in a discrete time framework. A model of the firm is described which includes the price-dividend balance integral equation whose solution yields the time path of share price, the number of outstanding shares, and the value of the firm. A broad class of firms for which the solution formula yields finite valued solution is characterized. This paper represents a rigorous mathematical treatment as well as a significant generalization of the Miller-Modigliani theory of the financial valuation. It is also shown that the arbitrage approach and the dividend approach to valuation of a firm are not equivalent. A precise condition which makes the equivalent is also obtained.