A Stochastic Extension of the Miller‐Modigliani Framework1

Suresh Sethi, N. A. Derzko and J. P. Lehoczky

Mathematical Finance, 1991, vol. 1, issue 4, 57-76

Abstract: 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 setting. the fundamental valuation approach under the assumption of risk neutrality is used to obtain the time path of 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. the results are extended to the non‐risk‐neutral case. A regularity condition, which is both necessary and sufficient for the share price to equal the capitalization of future dividends accruing to the share, is obtained. As a mathematical aside, it is shown in the appendix that in the absence of this condition, the so‐called stream of dividends approach is meaningless in the sense that it does not yield any financial valuation.

Date: 1991
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