Many infinite-horizon optimal control problems in management science and economics have optimal paths that approach some stationary level. Often, this path has the property of being the nearest feasible path to the stationary equilibrium. This paper obtains a simple multiplicative...

Dynamic modeling is general and recently the most interesting perspective to solve a dynamic economic problem based on Pontryagin’s maximum principle. Moreover, according to traditional economic theory, up to the middle of twentieth century, production functions are built without taking into...

We study a continuous-time problem of optimal public good contribution under uncertainty for an economy with a finite number of agents. Each agent can allocate his wealth between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study...

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on...

Dynamic rational inattention problems used to be difficult to solve. This paper provides simple, analytical results for dynamic rational inattention problems. We start from the benchmark rational inattention problem. An agent tracks a variable of interest that follows a Gaussian process. The...

Dynamic rational inattention problems used to be difficult to solve. This paper provides simple, analytical results for dynamic rational inattention problems. We start from the benchmark rational inattention problem. An agent tracks a variable of interest that follows a Gaussian process. The...

This paper proposes and solves an optimal dividend problem in which a two-state regimeswitching environment affects the dynamics of the company's cash surplus and, as a novel feature, also the bankruptcy level. The aim is to maximize the total expected profits from dividends until bankruptcy....

Nous présentons un exemple archétypal de jeu à champ moyen. Cet exemple est important à deux égards. Tout d'abord, il est suffisamment simple pour permettre l'obtention de solutions explicites : les fonctions de Bellman sont quadratiques, les mesures stationnaires gaussiennes et l'étude de...

In this article, we present a reference case of mean field games. This case can be seen as a reference for two main reasons. First, the case is simple enough to allow for explicit resolution: Bellman functions are quadratic, stationary measures are normal and stability can be dealt with...

What is an optimal or a sustainable external debt - for a country, region or sector? How should one monitor and evaluate debt to preclude a crisis? We use stochastic optimal control/dynamic programming to derive an optimal debt. The deviation of the actual from the optimal will serve as a...