Age-structured optimal control in population economics

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotkatype renewal model of population dynamics is combined with a Solow/Ramsey economy. By using a new maximum principle for distributed parameter control we derive meaningful qualitative results for the optimal migration path and the optimal saving rate.

Workshop on "Age-structured models in population dynamics and economics at the Vienna Institute of Demography, October 27-28, 2003

not found!

Adaptive Model-Predictive Climate Policies in a Multi-Country Setting

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2012.29 - ISSN : 1955-611XThe purpose of this paper is to extend the use of integrated assessment models by defining rational policies based on predictive control and adaptive behavior. The paper begins with an review of the main IAMs and their use. Then the concept of Model Predictive Nash Equilibrium (MPNE) is introduced within a general model involving heterogeneous economic agents operating in (and interfering with) a common environment. This concept captures the fact that agents do not have a perfect foresight for several ingredients of the model, including that of the environment. A version of the canonical IAM (DICE) is developed as a benchmark case. The concept of MPNE is then enhanced with adaptive learning about the environmental dynamics and the damages caused by global warming. The approach is illustrated by some numerical experiments in a two-region setting for several scenarios.L'objectif de cet article est d'inclure dans un modèle d'estimation intégrée (IAM) des politiques rationnelles basées sur les théories de contrôle optimal et de comportement adaptatif. L'article commence avec une revue des IAMs les plus importantes et leur utilisation dans la littérature. Par la suite, nous introduisons le concept d'Equilibre de Nash dans le cas d'un Modèle Prédictif (MPNE) et l'intégrons à un modèle général comprenant des agents économiques hétérogènes qui agissent (et qui interfèrent) dans un même milieu. Ce concept reprend des agents qui n'ont pas de "perfect foresight" par rapport à différents ingrédients du modèle, y compris l'environnement. Une version du DICE, le modèle IAM canonique, est développé comme modèle cadre. Le concept de MPNE est alors amélioré à travers un processus d'apprentissage adaptif concernant la dynamique de l'environnement et les dommages induits par le changement climatique. Notre approche est illustrée au moyen de plusieurs simulations numériques dans un cadre à deux régions

Solution stability of parabolic optimal control problems with fixed state-distribution of the controls

The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The control has a predefined spatial distribution and only the magnitude at any time is a subject of choice. The obtained conditions for subregularity imply, in particular, sufficient optimality conditions that extend the known ones. The paper is complementary to a companion one by the same authors, in which a distributed control is considered.Comment: arXiv admin note: substantial text overlap with arXiv:2209.0892

On the solution stability of parabolic optimal control problems

The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for problems in which the equation and the objective functional are affine with respect to the control. The perturbations may appear in both the equation and in the objective functional and may non-linearly depend on the state and control variables. The main results are based on an extension of recently introduced assumptions on the joint growth of the first and second variation of the objective functional. The stability of the optimal solution is obtained as a consequence of a more general result obtained in the paper -- the proved metric subregularity of the mapping associated with the system of first-order necessary optimality conditions. This property also enables error estimates for approximation methods. Lipschitz estimate for the dependence of the optimal control on the Tikhonov regularization parameter is obtained as a by-product

Optimal Harvesting Time in Fish Farming with Heterogenous Population

The optimal harvesting time in a fish farm is analyzed in the paper. Fish population is assumed to be heterogeneous with respect to weight, so a distributed parameter dynamic model is considered. Theoretical and numerical results are obtained and compared with the ones concerning homogeneous fish cultures only. The results are applied to the tilapia farming in Mexico for which empirical and market data were obtained. The actual managerial practices turn out to be close to the optimal solution in the model where weight-heterogeneity of the culture is taken into account

An immuno-epidemiological model with waning immunity after infection or vaccination

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of a system of first order partial differential equations, involving nonlinear integral terms and different transfer velocities. Structurally, the equation may be interpreted as a Fokker-Planck equation for a piecewise deterministic process. However, unlike the usual models, our equation involves nonlocal effects, representing the infectivity of the whole environment. This, together with the presence of different transfer velocities, makes the proved existence of a solution novel and nontrivial. In addition, the asymptotic behavior of the model is analyzed based on the obtained qualitative properties of the solution. An optimal control problem with objective function including the total number of deaths and costs of vaccination is explored. Numerical results describe the dynamic relationship between contact rates and optimal solutions. The approach can contribute to the understanding of the dynamics of immune responses at population level and may guide public health policies.Austrian Science Fundhttp://dx.doi.org/10.13039/50110000242

Heterogeneous consumption in OLG model with horizontal innovations

The paper develops a general equilibrium endogenous growth model involving heterogeneous consumption by an age-structured population with uncertain but limited life span and balanced life-time budget without bequests. The heterogeneity is introduced via weights which the individuals attribute in their utility function to consumption of different goods depending on the vintage of the good. The goods are produced by monopolistically competitive firms and the variety of available goods/technologies is determined endogenously through R&D investments. A competitive bank sector provides financial resources for investments, secured by agents’ savings and future firms profits. The general equilibrium is characterized by a system of functional equations and is analytically or numerically determined for several particular weight functions. It is shown that the investments by agents alone may be insufficient to sustain growth, while additional investments provided by the bank sector may lead to growth. The resulting imbalance between agents’ assets and the total value of firms can grow unboundedly in the case of homogeneous consumption. The results exhibit the qualitative difference between the dynamics of the model with heterogeneous versus homogeneous consumption. In particular heterogeneous con- sumption (when old goods are discounted) reduces the additional investments by the financial sector so that the values of firms become balanced by the assets of agents in the long run.info:eu-repo/semantics/publishedVersio

Relaxation of Euler-Type Discrete-Time Control System

This paper investigates what is the Hausdorff distance between the set of Euler curves of a Lipschitz continuous differential inclusion and the set of Euler curves for the corresponding convexified differential inclusion. It is known that this distance can be estimated by O( √ h), where h is the Euler discretization step. It has been conjectured that, in fact, an estimation O(h) holds. The paper presents results in favor of the conjecture, which cover most of the practically relevant cases. However, the conjecture remains unproven, in general