Stochastic growth: a duality approach

We re-examine the representative agent's optimal consumption and savings under uncertainty in the presence of investment constraints using martingale representation and convex analysis techniques. This framework allows us to explicitly quantify precautionary savings which induces a higher average growth rate than in a certainty setup. We provide a closed form solution for a Cobb-Douglas economy. The effect of uncertainty on portfolio selection is analyzed. Consumption growth rate and risk free interest rate exhibit a U-shaped relationship. Uncertainty negatively affects expected consumption growth rate; such a result seems to be supported by empirical evidence.     

Entry and growth in a perfectly competitive vintage model

A perfectly competitive vintage-knowledge model of Schumpeterian growth is introduced to study the relation between growth, technology-lifetime, entry, and productivity-dispersion. The incentive to innovate is generated by the productivity-dispersion (latent in traditional vintage models) between new and old plants, rather than by monopoly rents. The model has a unique steady-state REE with endogenous growth. The endogenous extent of entry constitutes a buffer, dampening the effect of research-efficiency and completely neutralizing the effect of population size or population growth rates on per-capita income levels and growth rates. Variations of research-efficiency lead to a negative relation between growth and vintage-lifetime and a non-monotonic relation between growth and productivity-dispersion.     

Intertemporal Equity and Hartwick's Rule in an Exhaustible Resource Model*

In a standard exhaustible resource model, it is known that if, along a competitive path, investment in the augmentable capital good equals the rents on the exhaustible resource (known as Hartwick's rule), then the path is equitable in the sense that the consumption level is constant over time. In this paper, we show the converse of this result: if a competitive path is equitable, then it must satisfy Hartwick's rule.     

Hölder continuity of the policy function approximation in the value function approximation

We show that given a value function approximation V of a strongly concave stochastic dynamic programming problem (SDDP), the associated policy function approximation is Hölder continuous in V.     

论"后过渡期"我国境外消费教育服务贸易

当前国际境外消费教育（留学生教育）服务贸易发展迅速，但也呈现出极端的不平衡，国际留学生市场基本上由发达国家垄断。在我国进入“入世后过渡期”阶段，借鉴发达国家经验大力发展境外消费教育服务贸易时应注意：加强质量和特色建设，积极解决留学生费用，针对外国留学生特点进行教学和组织科研，加强教育服务贸易相关问题研究等。     

Econometric analysis of linearized singular dynamic stochastic general equilibrium models

In this paper I propose an alternative to calibration of linearized singular dynamic stochastic general equilibrium models. Given an a-theoretical econometric model as a representative of the data generating process, I will construct an information measure which compares the conditional distribution of the econometric model variables with the corresponding singular conditional distribution of the theoretical model variables. The singularity problem will be solved by using convolutions of both distributions with a non-singular distribution. This information measure will then be maximized to the deep parameters of the theoretical model, which links these parameters to the parameters of the econometric model and provides an alternative to calibration. This approach will be illustrated by an application to a linearized version of the stochastic growth model of King, Plosser and Rebelo.     

Voting in assemblies of shareholders and incomplete markets

Summary. An economy with two dates is considered, one state at the first date and a finite number of states at the last date. Shareholders determine production plans by voting - one share, one vote - and at -majority stable stock market equilibria, alternative production plans are supported by at most percent of the shareholders. It is shown that a -majority stable stock market equilibrium exists if where S is the number of states at the last date and J is the number of firms. Moreover, an example shows that -majority stable stock market equilibria need not exist for smaller s.Received: 23 December 2002, Revised: 14 June 2004, JEL Classification Numbers: D21, D52, D71, G39. Correspondence to: Hervé CrésThe authors are grateful to an anonymous referee for helpful comments and suggestions. Financial support from the Danish Research Councils and hospitality of HEC is gratefully acknowledged by Mich Tvede and support from Fondation HEC is gratefully acknowledged by Hervé Crés.     

Mean-variance hedging for interest rate models¶with stochastic volatility

The mean-variance hedging approach for pricing and hedging claims in incomplete markets was originally introduced for risky assets. The aim of this paper is to apply this approach to interest rate models in the presence of stochastic volatility, seen as a consequence of incomplete information. We fix a finite number of bonds such that the volatility matrix is invertible and provide an explicit formula for the density of the variance-optimal measure which is independent of the chosen times of maturity. Finally, we compute the mean-variance hedging strategy for a caplet and compare it with the optimal stategy according to the local risk minimizing approach. Received: 14 July 2000 / Accepted: 10 April 2001     

Optimal growth and cycles in overlapping generations models

Summary This paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.We thank C. Blackorby, J. Blot, P. Cartigny and one anonymous referee for helpful comments and suggestions which generally improved the exposition of the paper. We would also like to thank the participants of the Population and demography session of the European Economic Association 10th Annual Congress (Prague, The Czech Republic, September 1–4, 1995).