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Infinite Horizon Programs

Econometrica 1981 49(3), 679
[This paper presents a general framework for the analysis of programs over an infinite horizon in continuous time. Sufficient conditions for the existence of an optimal program are derived and are shown to reduce to the condition that the underlying preference ordering exhibit impatience in a topology determined by the underlying technology.]

Optimal Portfolio Insurance

Journal of Financial and Quantitative Analysis 1981 16(3), 279
The form of the Pareto optimal general insurance contract has been investigated by Borch [5], Arrow [3], and Raviv [16]. This paper extends their work to the consideration of the optimal investment portfolio insurance contract. This is a contract whose payoff depends upon the investment performance of some specified portfolio of common stocks. Portfolio insurance differs from general insurance in two important ways. First, investment portfolio insurance lacks the property of stochastic independence between losses on different contracts which is characteristic of general insurance, and this has led some actuaries to question whether portfolio insurance contracts should be sold in view of the risks they pose for the solvency of insurance companies. Recent developments in the theory of option pricing suggest, however, that under certain assumptions an insurance company will be able to eliminate the risks associated with portfolio insurance contracts by following an appropriately defined investment strategy. Secondly, there exists a market for the pricing of investment risks, the securities market; and, under appropriate assumptions, the equilibrium price of portfolio insurance contracts may be determined without specification of the preferences of insurance companies. This permits consideration of insurance company preference functions to be dispensed with, in marked contrast to the earlier literature concerned with general insurance, which treats insurance company preferences symmetrically with those of the insurance purchaser. In addition, since the characteristics of the insured portfolio are known to the insurer, and the performance of the portfolio is beyond the control of the insured, portfolio insurance is not prone to the problems of adverse selection and moral hazard which are liable to arise in general insurance.

Investment in Finished Goods Inventories: An Analysis of Adjustment Speeds

American Economic Review 1981
It is well known that fluctuations in inventory investment are a major source of fluctuations in gross national product. This has stimulated numerous empirical studies designed to understand the causes of changes in inventory investment. These studies include those (for example, Michael Lovell) that utilize a flexible accelerator model of inventory behavior as well as those (for example, David Belsley) that utilize the linear decision rule approach to optimal inventory holding. The latter approach, however, can be interpreted in terms of a flexible accelerator model. See J. C. R. Rowley and P. K. Trivedi for a survey of the literature. Recently, several authors (for example, Martin Feldstein and Alan Auerbach) observed that these studies yield very implausible empirical results. The basic difficulty is that the estimates of the speed with which firms close gaps between desired and actual inventory stocks are very low. Often, the estimated speed of adjustment is less than 10 percent per quarter. As Feldstein and Auerbach stress, this is extremely implausible when even the largest swings in inventories in a given quarter amount to less than one day's production. The purpose of this paper is to undertake an analysis of adjustment speeds for finished goods inventory investment. In our empirical work, we utilize a modified flexible accelerator model of inventory investment.1 Like the conventional flexible accelerator, the model permits firms to close a fraction of the gap between desired and actual inventories in any period. The relevant fraction is of course the adjustment coefficient, and it may vary in principle between zero and unity. Our model differs from the conventional model in assuming that the desired stock of finished goods inventories depends on the normal levels of exogenous variables that firms must forecast to make decisions on inventory holdings. These include not only the normal level or orders, or demand, which is a standard explanatory variable in the empirical literature, but also the normal levels of real factor-input prices and real interest rates. In addition, we permit the normal levels to change relatively slowly in response to changes in past levels of orders, real factor-input prices, and real interest rates. Our objective is to investigate whether the slow adjustment speeds that have been estimated in the literature are due to the use of models which contain an incomplete menu of exogenous variables to determine desired inventories and pay inadequate attention to lags in the adjustment of normal levels of exogenous variables.