by Yves Achdou, Pierre-Noel Giraud, Jean-Michel Lasry & Pierre-Louis Lions

A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problems with two controls, first the ux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton-Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to t the historical data is carried out.

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by Céline Grislain-Letrémy & Bertrand Villeneuve

The industrialists are liable for any damage they cause to neighboring households. Consequently, households do not have to pay for the risk they create by locating in exposed areas. To contain their liabilities, the firm can purchase or rent land, establishing an exclusion zone, also called a red zone. This paper studies the negotiations of red zones in urban areas exposed to industrial disasters. We compare typical scenarios regarding the distribution of bargaining power between the firm and the city. Using a microeconomic model, we explain how red zones are revised as technology, climate, or demography change, and we show how and why responses are neatly distinct across scenarios. Further, we give and explain the conditions for industrial sanctuaries (as the population grows) and city cores (as the risk grows).

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by Céline Grislain-Letrémy & Bertrand Villeneuve

This paper addresses the urbanization of areas exposed to natural disasters and studies its dependency on land-use and insurance policies. The risk-map paradox that we describe explains why an insurance system with simplistic maps and tariffs is the rule. Indeed, in practice we observe simple policies, consisting of a prohibited red zone and a zone without insurance tariff differentiation. We show that they implement the optimal land-use in specific cases. Even if there are fixed damages per dwelling, the red-zone policy is relatively efficient. In a central proposition, we detail the effects redefining the optimal red zone as the climate or the population changes. We use this analysis to expose and comment plausible cases in which, as the population grows, the red zone shrinks, the red zone grows, and the red zone shrinks and then grows.

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par Henri Verdier & Charles Murciano 

Cet article interroge l’actualité intellectuelle et légale des communs. Plus précisément, notre travail explore la notion de commun numérique (ou informationnel) et ses spécificités au regard du concept classique de communs en théorie économique. Les communs numériques désignent les nouveaux modes d’administration d’une ressource informationnelle par une communauté, qui sont permis par les technologies de l’information et de la communication. Ils constituent un mode de partage de ressources socialement valorisées. Les économistes s’accordent sur une conception classique des biens communs, désignant une ressource rivale et non-exclusive. Les communs numériques étant immatériels, cette définition est insatisfaisante. En outre, les travaux d’Elinor Ostrom ont souligné la dualité des communs, à la fois ressource exploitée en commun et régime de droits de propriété dérogeant au paradigme de la propriété privée. Notre article spécifie ainsi cette ambivalence à l’ère numérique. L’examen attentif d’exemples de communs numériques promus par l’Etat permet d’expliciter la logique contributive à l’oeuvre dans ces communs. Nous soutenons que cette logique autorise une nouvelle forme d’action publique. Alliée à la « multitude », en promouvant et en encadrant les communs, la puissance publique pourrait s’armer contre l’hégémonie croissante de grandes plateformes monopolistiques, dont les logiques s’opposent de plus en plus à celles des Etats.

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by Henri Verdier and Charles Murciano

This paper addresses the current intellectual and legal status of the commons. Specifically, we explore the notion of the digital (or information) commons and its specificities with regard to the classic concept of the commons in economic theory. The digital commons concerns new ways of administering an information resource by a community, made possible by information and communications technology. It constitutes a means of sharing socially valued resources. Economists agree on a classic conception of common goods, designating a rival and non-exclusive resource. Because the digital commons is immaterial, this definition is unsatisfactory. In addition, the work of Elinor Ostrom emphasizes the duality of the commons: both a resource used in common and a property-rights regime running counter to the paradigm of private property. Our paper thus examines this ambiguity in the digital age. Careful study of examples of digital commons promoted by the state can clarify the contributory logic at work in these commons. We argue that this approach authorizes a new form of public action. Allied with the “multitude”, the public authorities could, by nurturing and supervising the commons, arm themselves against the growing hegemony of big monopolistic platforms, whose logic is increasingly opposed to that of the state.

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by Geir B. Asheim & Ivar Ekeland 

The Chichilnisky criterion is an explicit social welfare function that satisfies compelling conditions of intergenerational equity. However, it is time inconsistent and has no optimal solution in the Ramsey model. By investigating stationary Markov equilibria in the game that generations with Chichilnisky preferences play, this paper shows how nevertheless this criterion can be practically implemented in the Ramsey model, leading to attractive consequences. The time-discounted utilitarian optimum is the unique equilibrium path with a high-productive initial stock, implying that the weight on the infinite future in the Chichilnisky criterion plays no role. However, this part of the Chichilnisky criterion may lead to more stock conservation than the timediscounted utilitarian optimum with a low-productive initial stock. Based on the notion of von Neumann-Morgenstern abstract stability, we obtain uniqueness by assuming that each generation coordinates on an almost best equilibrium and takes into account that future generations will do as well.

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by Ivar Ekeland and Maurice Queyranne

In open pit mining, one must dig a pit, that is, excavate the upper layers of ground before reaching the ore. The walls of the pit must satisfy some mechanical constraints, in order not to collapse. The question then arises how to mine the ore optimally, that is, how to find the optimal pit. We set up the problem in a continuous (as opposed to discrete) framework, and we show, under weak assumptions, the existence of an optimum pit. For this, we formulate an optimal transportation problem, where the criterion is lower semi-continuous and is allowed to take the value +∞. We show that this transportation problem is a strong dual to the optimum pit problem, and also yields optimality (complementarity slackness) conditions.

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by Anthony Lecavil, Nadia Oudjane & Francesco Russo

We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the propagation of chaos. To this system, we associate a random function which is proved to converge to a solution of a regularized version of PDE.

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by Delphine Lautier, Franck Raynaud & Michel A. Robe

We apply the concepts of conditional entropy, information transfers and directed graphs to investigate empirically the propagation of price fluctuations across a futures term structure. We focus on price relationships for North American crude oil futures because this key market experienced several structural changes between 2000 and 2014: financialization (starting in 2003), infrastructure limitations (in 2008-2011) and regulatory changes (in 2012-2014) in addition to big demand and supply shocks in the underlying asset market. We find large variations over time in the amount of information shared by contracts with different maturities. Although on average short-dated contracts (up to 6 months) emit more information than backdated ones, a dynamic analysis reveals that, after 2012, similar amounts of information flow backward and forward along the futures maturity curve. The mutual information share increased substantially starting in 2004 but fell back sharply in 2012-2014. In the crude oil space, our findings point to a puzzling re-segmentation of the futures market by maturity in 2012-2014. More broadly, they have implications for the Samuelson effect and raise questions about the causes of market segmentation.

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by Delphine Lautier, Julien Ling and Franck Raynaud

We examine the impact of two financial crises on commodity derivative markets: the subprime crisis and the bankruptcy of Lehman Brothers. These crises are “external” to the commodity markets because they occurred in the financial sphere. Still, because commodity markets are now highly integrated with each other and with other financial markets, such events could have had an impact. In order to fully comprehend this possible impact, we rely on tools inspired by the graph theory that allow for the study of large databases. We examine the daily price fluctuations recorded in 14 derivative markets from 2000 to 2009 in three dimensions: the observation time, the space dimension – the same underlying asset can be traded simultaneously in two different places – and the maturity of the transactions. We perform an event study in which we first focus on the efficiency of the price shock’s transmission to the commodity markets during the crises. Then we concentrate on whether the paths of shock transmission are modified. Finally, relying on the measure proposed by Bonacich (1987) for social networks, we focus on whether the centrality of the price system changes.

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