In this paper, we tackle a generic optimal regime switching problem where the decision-making process is not the same from one regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a two-stage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for open-loop strategies with a linear state equation and linear-quadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using theoretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss reverse switching.
We investigate the link between resource revenues volatility and institutions. We build a stochastic differential game with two players (conservatives vs. liberals) lobbying for changing the institutions in their preferred directions. First, uncertainty surrounds the dynamics of institutions and the resource revenues. Second, the lobbying power is asymmetric, the conservatives’ power being increasing with resource revenues. We show the existence of a unique equilibrium in the set of affine strategies. We then examine to which extent uncertainty leads to more liberal institutions in the long run, compared to the deterministic case. We finally explore the institutional impact of volatility using a database covering 91 countries over the period 1973–2005. Focusing on financial liberalization, we find that as oil revenue volatility increases, liberalization goes down. This result is robust to different specifications and sample distinctions.
We study the joint determination of optimal investment and optimal depollution in a spatiotemporal framework where pollution is transboundary. Pollution is controlled at a global level. The regulator internalizes that: (i) production generates pollution, which is bad for the wellbeing of population, and that (ii) pollution flows across space driven by a diffusion process. We solve analytically for the optimal investment and depollution spatiotemporal paths and characterize the optimal long-term spatial distribution when relevant. We finally explore numerically the variety of optimal spatial distributions obtained using a core/periphery model where the core differs from the periphery either in terms of input productivity, depollution efficiency, environmental awareness or self-cleaning capacity of nature. We also compare the distributions with and without diffusion. Key aspects in the optimal policy of the regulator are the role of aversion to inequality, notably leading to smoothing consumption across locations, and the control of diffusive pollution adding another smoothing engine.
Does drawing economic benefit from nature impinge on conservation? This has been a subject of controversy in the literature. The article presents a management method to overcome this possible dilemma, and reconcile conservation biology with economics. It is based on recent advances in the mathematical theory of dynamic systems under viability constraints. In the case of a one-locus two-allele plant coexisting with a one-locus two-allele parasite, the method provides a rule for deciding when and to what extent the resistant or the susceptible strain should be cultivated, in the uncertain time-varying presence of the parasite. This is useful for preventing the fixation of the susceptible allele - and thereby limiting the plant's vulnerability in the medium term, should the parasite reappear. The method thus provides an aid to decision for economic and ecology-friendly profitability.
We solve a linear-quadratic model of a spatio-temporal economy using a polluting one-input technology. Space is continuous and heterogenous: locations differ in productivity, nature self-cleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatio-temporal functional is quadratic in local consumption and linear in pollution. Using a dynamic programming method adapted to our infinite dimensional setting, we solve the associated optimal control problem in closed-form and identify the asymptotic (optimal) spatial distribution of pollution. We show that optimal emissions will decrease at given location if and only if local productivity is larger than a threshold which depends both on the local pollution absorption capacity and environmental awareness. Furthermore, we numerically explore the relationship between the spatial optimal distributions of production and (asymptotic) pollution in order to uncover possible (geographic) environmental Kuznets curve cases.
We review the most recent advances in distributed optimal control applied to Environmental Economics, covering in particular problems where the state dynamics are governed by partial differential equations (PDEs). This is a quite fresh application area of distributed optimal control, which has already suggested several new mathematical research lines due to the specificities of the Environmental Economics problems involved. We enhance the latter through a survey of the variety of themes and associated mathematical structures beared by this literature. We also provide a quick tour of the existing tools in the theory of distributed optimal control that have been applied so far in Environmental Economics.
The pure risk sharing mechanism implies that financial liberalization is growth enhancing for all countries as the world portfolio shifts from safe low-yield capital to riskier high-yield capital. This result is typically obtained under the assumption that the volatilities for risky assets prevailing under autarky are not altered after liberalization. We relax this assumption within a simple two-country model of intertemporal portfolio choices. By doing so, we put together the risk sharing effect and a well-defined instability effect. We identify the conditions under which liberalization may cause a drop in growth. These conditions combine the typical threshold conditions outlined in the literature, which concern the deep characteristics of the economies, and size conditions on the instability effect induced by liberalization.
In this paper, we consider an abstract optimal control problem with state constraint. The methodology relies on the employment of the classical dynamic programming tool considered in the infinite dimensional context. We are able to identify a closed-form solution to the induced Hamilton-Jacobi-Bellman (HJB) equation in infinite dimension and to prove a verification theorem, also providing the optimal control in closed loop form. The abstract problem can be seen an abstract formulation of a PDE optimal control problem and is motivated by an economic application in the context of continuous spatiotemporal growth models with capital di usion, where a social planner chooses the optimal location of economic activity across space by maximization of an utilitarian social welfare function. From the economic point of view, we generalize previous works by considering a continuum of social welfare functions ranging from Benthamite to Millian functions. We prove that the Benthamite case is the unique case for which the optimal stationary detrended consumption spatial distribution is uniform. Interestingly enough, we also find that as the social welfare function gets closer to the Millian case, the optimal spatiotemporal dynamics amplify the typical neoclassical dilution population size effect, even in the long-run.