Dynamic optimization problems cover a great class of problems in theoretical and applied economics and technology. In this account the exploitation of a general renewable capital stock is modeled through an alternative formulation to the classical optimal control approach. We propose a very simple alternating iterative algorithm that is shown to converge very fast towards a solution, where the ...

We propose a duality approach to solving contracting models with either one-sided or two-sided limited commitment in continuous time. We establish weak and strong duality theorems and provide a dynamic programming characterization of the dual problem. The dual problem gives a linear Hamilton-Jacobi-Bellman equation with a known state space subject to free-boundary conditions, making analysis mu...

In this article, our objective is to determine efficient allocations in economies with multiple agents having recursive utility functions. Our main result is to show that in a multiagent economy, the problem of determining efficient allocations can be characterized in terms of a single value function (that of a social planner), rather than multiple value functions (one for each investor), as ha...

This paper analytically solves the Riccati equation of discrete optimal control with two targets and one tool. This is accomplished by reducing the problem to a nonlinear univariate dynamic equation; this can be solved by a suitable transformation of variable. Beyond its direct application to two-target economic problems, the present approach may provide insight toward the eventual solution of ...

This paper shows that the efficiency of relational contracting can be increased by reducing the public information through a novel intertemporalgarbling process of signals. A distinctive and essential feature of our intertemporalgarbling process is that past outputs have enduring effects on future signals. This process reduces the principal’s maximal reneging temptation by linking together the ...

Many separable dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for such value iteration to be con...

This paper extends the recent investigation of Tahvonen and Withagen (1996, Journal of Economic Dynamics and Control 20, 1775}1795) for costly and thus sluggish instead of instantaneous reductions in emissions. In addition to the social optimum, the paper investigates the competitive equilibrium. This plausible extension allows to derive limit cycles as the outcome for both, the social optimum ...

A dynamic model with learning and adaptation captures the evolution in trader beliefs and trading strategies. Through a process of learning and observation, traders improve their understanding of the market. Traders also engage in a process of adaptation by switching between trading strategies based on past performance. The asymptotic properties are derived analytically, demonstrating that conv...

Economists model time as continuous or discrete. The recent literature on continuous time models with delays should help to bridge the gap between these two families of models. In this note, we propose a simple time–to–build model in continuous time, and show that a discrete time version is a true representation of the continuous time problem under some sufficient conditions. JEL codes: O40, E3...

Using a long panel of roll call voting data, I find that “flip-flopping” senators face significant electoral costs when changing positions. In models of electoral competition, as the costs to candidates changing position approach zero, the equilibrium prediction is the convergence of platforms. Such convergence is at odds with empirical observation. Using a dynamic, structural model of candidat...