Impatience and dynamic optimal behavior: A bifurcation analysis of the Robinson-Solow-Srinivasan model

This paper provides a study of optimal economic growth under discounting in discrete time in a two-sector version of the Robinson-Solow-Srinivasan model. It examines how dynamic optimal behavior changes in response to increasing impatience. The optimal policy function is a pan map for high discount factors and a check map for low discount factors. It is shown that the transformation from the pan map to the check map, for the intermediate range of discount factors, can be quite intricate. This is demonstrated by proving the existence of two bifurcation values of the discount factor in the borderline case of the model, which establishes the possibility of reswitching of optimal actions as the discount factor varies.     

THE OPTIMAL ALLOCATION ABOUT CAPITAL AND LABOR IN THE ECONOMIC GROWTH WITH AN ENDOGENOUS TECHNICAL PROGRESS MODEL

In this paper, the balanced economic growth path was considered in a new growth model with endogenous technical progress. It is not only obtained the optimal allocation about capital and labor between a goods-producing sector and a R&D Sector, but also the optimal value of saving rates. By discussing the effect of parameters, it are also got the following results: When the rate of time preference (discount factor) rising, the fractions of Capital and labor in the goods-producing sector will increase , the fractions in R&D sector and the saving rates will decrease; When the population grows rapidly, the result will be contrary.     

IBN and Related Properties for Rings

We first tackle certain basic questions concerning the Invariant Basis Number (IBN) property and the universal stably finite factor ring of a direct product of a family of rings. We then consider formal triangular matrix rings and obtain information concerning IBN, rank condition, stable finiteness and strong rank condition of such rings. Finally it is shown that being stably finite is a Morita invariant property.     

IBN and Related Properties for Rings

We first tackle certain basic questions concerning the Invariant Basis Number (IBN) property and the universal stably finite factor ring of a direct product of a family of rings. We then consider formal triangular matrix rings and obtain information concerning IBN, rank condition, stable finiteness and strong rank condition of such rings. Finally it is shown that being stably finite is a Morita invariant property. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cost minimization and the stochastic discount factor

It is shown that a cost function subject to internal costs of adjustment induces a stochastic discount factor (pricing kernel) that is a function of random output, input and output prices, existing capital stock, and investment. The only assumption on firm preferences is that they are increasing in current period consumption and future stochastic consumption. This ensures that the firm will always act to minimize current period cost of providing future consumption, and it is the first-order conditions for this cost minimization problem that generate the stochastic discount factor, which itself can be interpreted as the marginal variable cost of varying stochastic output. A cost-based pricing kernel is estimated using annual time-series data on macroeconomic variables and returns data for the S&P 500 and commercial paper.     

THE INTRINSIC QUALITATIVE PROPERTIES OF THE CLASSICAL OPTIMAL STOPPING PROBLEM ARE INVARIANT TO THE FUNCTIONAL FORM OF THE DISCOUNT FUNCTION

Abstract The intrinsic qualitative properties of a generic optimal stopping model are shown to be invariant to the functional form of the discount function. If the discount function is assumed to be a member of particular infinite parametric family—a family that includes the exponential and classical hyperbolic discount functions as special cases—an additional refutable comparative statics result is produced that holds for the entire family. Consequently, if one limits econometric tests of the model to its qualitative properties, one cannot determine the form of the discount function used by the decision maker. It is also shown that the only discount function that yields a time‐consistent stopping rule is the exponential function with a constant rate of discount.     

Default Times in a Continuous Time Markov Chain Economy

Abstract

A continuous time financial market is considered where randomness is modelled by a finite state Markov chain. Using the chain, a stochastic discount factor is defined. The probability distributions of default times are shown to be given by solutions of a system of coupled partial differential equations.     

基于资本约束的资本机会成本定价研究

资本约束与信息不对称密切相关 ,当企业内部存在信息不对称时 ,企业实施内部资本约束 ,此时 ,由于外部资本市场能够产生正确的资本机会成本信号 ,净现值准则可以用于项目选择 .而当企业外部资本市场存在信息不对称时 ,资本提供者会实施外部资本约束 ,由于信息不对称歪曲了资本机会成本的市场信号 ,净现值准则失效 ,此时 ,机会成本的定价研究需要引进效用函数及主观资本回报率等工具 .     

Asset allocation,sustainable withdrawal,longevity risk and non-exponential discounting

The present paper studies an optimal withdrawal and investment problem for a retiree who is interested in sustaining her retirement consumption above a pre-specified minimum consumption level. Apparently, the withdrawal and investment policy depends substantially on the retiree’s health condition and her time preferences (subjective discount factor). We assume that the health of the retiree can worsen or improve in an unpredictable way over her lifetime and model the retiree’s mortality intensity by a stochastic process. In order to make the decision about the consumption and investment policy more realistic, we assume that the retiree applies a non-exponential discount factor (an exponential discount factor with a small amount of hyperbolic discounting) to value her future income. In other words, we consider an optimization problem by combining four important aspects: asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting. Due to the non-exponential discount factor, we have to solve a time-inconsistent optimization problem. We derive a non-local HJB equation which characterizes the equilibrium optimal investment and consumption strategy. We establish the first-order expansions of the equilibrium value function and the equilibrium strategies by applying expansion techniques. The expansion is performed on the parameter controlling the degree of discounting in the hyperbolic discounting that is added to the exponential discount factors. The first-order equilibrium investment and consumption strategies can be calculated in a feasible way by solving PDEs.     

Solution of a Markovian decision problem by successive overrelaxation

Summary It is shown that successive overrelaxation can be applied in solving a discounted Markovian decision problem. An overrelaxation factor yielding minimum contraction factor is determined. The minimum contraction factor turns out to be at most equal to the discount factor.

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Zusammenfassung Es wird gezeigt, daß sukzessive Überrelaxation zur Lösung eines diskontierten Markoffschen Entscheidungsproblems herangezogen werden kann. Ein Überrelaxationsfaktor, der den minimalen Kontraktionsfaktor liefert, wird bestimmt. Der minimale Kontraktionsfaktor erweist sich als höchstens gleich dem Diskontierungsfaktor.