General Solution of the Stochastic Price-Dividend Integral Equation: A Theory of Financial Valuation

Abstract

This paper deals with the problem of the financial valuation of a firm and its shares of stock with given financing policies in a general stochastic environment. A model of the firm is described which includes the price-dividend balance integral equation whose solution yields the time path of the share price, the number of outstanding shares and the value of the firm. These are shown to be the unique conditional expectations of certain stochastic processes. A broad class of firms for which the solution formula yields finite valued solutions is characterized. This paper represents a rigorous mathematical treatment, as well as a significant stochastic extension of the Miller-Modigliani theory of financial valuation. It is also shown that the cash-flow approach and the dividend approach to valuation of a firm are not equivalent in general. A precise condition, which makes them equivalent, is also obtained.

Keywords: Price-Dividend Equation, Theory of Financial Valuation, Miller-Modigliani theory, MM theory, stochastic firm, integral equations, cash-flow approach, dividend approch, share price, tranversality condition, martingales, arbitrage, partial equilibrium, share repurchase, risk aversion, risk neutrality

JEL Classification: C61, M2, G3,G1, G12, G3, G31, G35, D40, D46