[The multi-period control problem analyzed assumes the data are generated by the simple regression model with an unknown slope coefficient. There is a tradeoff between stabilization and experimentation to learn more about the unknown coefficient. When parameter uncertainty is large, experimentation becomes an important consideration.]

[An exact discrete model is derived from a recursive model consisting of a set of rth order stochastic linear differential equations with constant coefficients such that observations generated at equidistant points of time by the differential system satisfy the discrete model irrespective of the length of sampling interval. The difficulty of estimating the exact model subject to a priori restrictions makes it necessary to approximate the differential system by a non-recursive discrete model that maintains the structural form. This discrete model has a moving average disturbance term of order r - 1, but the co-variance function of this process is approximated by a function that is independent of the parameters of the continuous model. The eigenvalues and eigenvectors of the approximations to the differential system as well as their asymptotic variance matrices are also derived but, like the approximate asymptotic variance matrices of the parameter estimates, these variances are about biased probability limit]

Robert H. Litzenberger, C. U. Rao, Portfolio Theory and Industry Cost of Capital Estimates, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1443-1462

[It is now popular to construct economic models in differential equation form. Perhaps the most serious econometric problem faced when dealing with a differential equation system is the practical difficulty of finding consistent estimates of the important structural parameters. In this paper a simple three-equation Phillips model is considered and consistent estimates of the structural parameters are provided by the minimum-distance procedure. The small-sample distributions of these estimates are investigated by the Monte Carlo method; and the results are then compared with those of the three-stage least-squares estimates found by making a discrete approximation to the system of differential equations.]

John C. G. Boot, George M. Frankfurter, The Dynamics of Corporate Debt Management, Decision Rules, and Some Empirical Evidence, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 4 (Sep., 1972), pp. 1957-1965

Abstract This article presents information on evaluating alternative methods of accounting for long-term nonsubsidiary holdings of common stock. Long-term investments by one corporation (investor) in the common stock of another corporation (investee) can be classified in one of two basic categories according to the percentage of the common stock of the investee corporation held by the investor corporation. Holdings of more than 50 percent are classified as subsidiary holdings while holdings of 50 percent or less are classified as nonsubsidiary holdings. Under the cost method, "periodic investor income" consists of dividends received by the investor which are distributed from the investor's proportionate share of undistributed investee earnings accumulated since the acquisition of the investment. The book value of the investment on the investor's books, hereafter referred to as "investment carrying value," is periodically reduced by any dividends received in which distributions in excess of investee earnings since acquisition of the investment. Such dividends are referred to in this paper as "excess dividends." Finally, Opinion 18 states that a senes of operating losses of an investee or other factors may indicate that a decrease in value of the investment has occurred which is other than temporary and should accordingly be recognized.

Abstract : The report presents an introduction to some of the concepts and results currently popular in optimal control theory. The introduction is intended for someone acquainted with ordinary differential equations and real variables, but with no prior knowledge of control theory. The material covered includes the problems of controllability, controllability using special (e.g., bang-bang) controls, the geometry of linear time optimal processes, general existence of optimal controls, and the Pontryagin maximum principle. (Author)