L’article modélise un programme de gestion de déchets nucléaires à haute activité. La physique du refroidissement permet d’entreposer un certain temps un colis chaud afin d’économiser le volume de stockage définitif : en effet, les colis plus froids peuvent être davantage serrés. La durée optimale théorique d’entreposage sans contrainte est caractérisée. Les diverses contraintes (contrainte sur la capacité de stockage, contrainte sur la durée d’entreposage, contrainte sur la capacité d’entreposage) sont envisagées. Elles conduisent à des traitements très différenciés selon les millésimes.

## Stratégie optimale de stockage de déchets radioactifs à vie longue sous contrainte de capacité

## The Ocean as a Global System

Available at www.amazon.fr

**The Ocean as a Global System: Economics and Governance of Fisheries and Energy Resources**

This book gathers together contributions from the Symposium “The Ocean: Green Shipping and Sustainable Energy”, held in Paris on 28-29 April 2011. The aim of the conference was to address critical issues regarding the ocean, considered successively as a global ecosystem, as a global energy system and as a global regulation system. The first part of the book is concerned with the current state and the future of fisheries. The second part deals with energy-related maritime activities, while the third offers a global perspective on these issues.

Ivar Ekeland, Damien Fessler, Jean-Michel Lasry et Delphine Lautier, The Ocean as a Global System, Economics and Governance of Fisheries and Energy Resources, Eska, 2012.

## A simple equilibrium model for a commodity market with spot trades and futures contracts

**by Ivar Ekeland, Delphine Lautier & Bertrand Villeneuve**

We propose a simple model which offers a unified theoretical framework for the analysis of price and quantity relationships in commodity markets. We study the simultaneous equilibrium in the physical and futures markets. We demonstrate the existence and uniqueness of this equilibrium and we provide explicit expressions. We provide insights into the hedging function of the futures market and the informational role of prices. The model is particularly efficient for precise qualitative and quantitative comparative statics. Among other possibilities, we compare equilibrium variables with and without futures markets and we show that the level and volatility of spot prices increases with the number of speculators. We also provide neat predictions on the political economy of potential reforms of market structure.

## The Economics of Sustainable Development

**Available at www.amazon.fr**

This book brings together the lecture notes from the seminars held at the Finance and Sustainable Development Chair from 2007 to 2009. The first part is concerned with climate change policies, with particular emphasis on the relevance of traditional economic theories. The second part deals with economic concepts and methodologies associated with sustainable development. It presents the precautionary principle, discusses the concept of externalities and introduces the methodology of mean field games. The third part is devoted to models and empirical applications in various fields, such as water resources, gas emissions, and a sustainable development path. The fourth part deals with carbon markets, along with their theoretical justification and historical development. The last part focuses on socially responsible investment and gives insights in regard to its definition, its links with sustainable development, and the way it could be used for investment strategies.

Jean-Michel Lasry, Delphine Lautier & Damien Fessler (editors), The Economics of Sustainable Development, Economica, 2010

## Optimal selling rules for monetary invariant criteria: tracking the maximum of a portfolio with negative drift

**by Romuald ELIE & Gilles-Edouard ESPINOSA**

Considering a positive portfolio diffusion X with negative drift, we investigate optimal stopping problems of the form (…) This paper unifies optimal selling rules observed by [5] for quadratic absolute distance criteria with bang-bang type ones observed in [1, 4, 9]. More precisely, we provide a verification result for the general stopping problem of interest and derive the exact solution for two classical criteria f of the literature. (…). These results reinforce the idea that optimal stopping problems of similar type lead easily to selling rules of very different nature. Nevertheless, our numerical experiments suggest that the practical optimal selling rule for the relative quadratic error criterion is in fact very close to immediate selling.

## Exact replication under Delta constraints

**by Jean-François Chassagneux, Romuald Elie & Idris Kharroubi**

This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value, which dominates the claim of interest, is the so-called facelift transform of the claim. We investigate under which conditions the super-replication price and strategy of a large class of claims coincide with the exact replication price and strategy of the facelift transform of this claim. In dimension 1, we observe that this property is satisfied for any local volatility model. In any dimension, we exhibit a necessary and sufficient condition for this property, which combines the dynamics of the stock together with the characteristics of the closed convex set of constraints. The obtention of this condition relies on the introduction of the notion of first order viability property for linear parabolic PDEs. We investigate in details several practical cases of interest: multidimensional Black Scholes model, non-tradable assets or short selling restrictions.

## Economic growth and sustainable development: how should we discount the future?

**by Qinglong Zhou, Ivar Ekeland, Yiming Long**

In 1987, the Brundtland Commission famously defined sustainable development as “developmentthat meets the needs of the present without compromising the needs of the future”. This paper is concerned with translating this definition in the framework of the neoclassical one-sector model of economic growth. We investigate and compare three possible criteria for sustainable development. The first one, which was introduced by Chichilnisky, the second one, which was introduced by Ekeland and Lazrak, and the third one, which goes back to Ramsey himself. We define and investigate equilibrium strategies. For the Chichilnisky criterion, there is a unique equilibrium strategy, which is just the optimal strategy for the neoclassical model. In the other two cases, there is a continuum of equilibrium strategies. We conclude that the most satisfying candidates for sustainable development are the equilibrium strategies for the third criterion (H-criterion).

## The Flood Issue: Uniform Insurance and Collective Prevention with Risk Externalities

**by Céline Grislain-Letrémy & Sabine Lemoyne de Forges**

Prevention policies against flood, such as dams or levees, are commonly designed by local jurisdictions and for most they exert externalities on neighboring jurisdictions. Each jurisdiction chooses its collective prevention effort depending on the insurance system that covers its inhabitants. As uniform insurance depends on all insureds’ risk, it enables a partial integration of prevention externalities by jurisdictions. We determine under which condition uniform insurance Pareto dominates actuarial insurance.

## Systemic Risk in Energy Derivative Markets: A Graph-Theory Analysis

**Delphine Lautier & Franck Raynaud**

This article uses graph theory to provide novel evidence regarding market integration, a favorable condition for systemic risk tio appear in. Relying on daily futures returns covering a 12-year period, we examine cross- and inter-market linkages, both within the commodity complex and between commodities and other financial assets. In such a high dimensional analysis, the graph theory enables us to understand the dynamic behavior of our price system. We also establish that crude oil is itself at the center of the energy complex. Further, we provide evidence that commodity markets are becoming more integrated over time.

## Risk-Parameter Estimation in Volatility Models

.

by **Christian Franck & Jean-Michel Zakoïan**

## Ecological intuition versus Economic “reason”

by **Olivier Guéant, Roger Guesnerie & Jean-Michel Lasry**

This article discusses the discount rate to be used in projects that aimed at preserving the environment. The model has two di§erent goods, one is the usual consumption good whose production may increase exponentially, the other is an environmental good whose quality remains limited. The stylized world we describe is fully determined by four parameters reáecting basic preferences, “ecological” and intergenerational concerns and feasibility constraints. We define an ecological discount rate and examine its connections with the usual interest rate and the optimized growth rate. We discuss, in this simple world, di§erent forms of the precautionary principle and show that cost-beneÖt analysis should overweigh in a spectacular way the probabilities of the events associated with bad environmental outcomes.

## A note on super-hedging for investor-producers

We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods. This general framework covers the interesting case of an electricity producer who wants to hedge a financial position and can trade commodities which are also inputs for his system. This extends the framework of (Bouchard and Nguyen, 2011) to continuous time for concave and bounded production functions. We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of (Rasonyi, 2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general setting. Using standard separation arguments, we then deduce a dual characterization of the latter.

## Journée de la Chaire FDD et du Laboratoire FIME

**6 décembre 2011 – ****EDF R&D – site de Clamart
**Cette journée consacrée à la présentation des travaux de recherche réalisés dans le cadre de la Chaire Finance et Développement Durable et du Laboratoire de Finance des Marchés de l’Energie a été organisée cette année dans les locaux de EDF R&D (site de Clamart). Une partie de la journée étaité consacrée à la présentation du bilan des 5 premières années de la Chaire et du Laboratoire.

supports des présentations des différentes sessions sur le site du laboratoire FIME

## Natural and Industrial Disasters: Land Use and Insurance

by **Céline Grislain-Letrémy & Bertrand Villeneuve**

Uncontrolled urbanization in exposed areas increases the cost of natural and industrial disas- ters. In the case of industrial risks, these land use externalities are directly exerted on the firm which is liable for the disaster. In the case of natural risks, the externalities take the form of free- riding on the mutualization mechanism. Land use policy and insurance can provide incentives to internalize these externalities. However these tools cannot be more precise than the hazard map on which they are based. We describe the efficiency gains of refining hazard categories, keeping in mind that they should be balanced with assessment costs. We determine the impact of climate change and demographic evolution on the equilibrium. Our results are established for a spectrum of alternative scenarios with various distributions of bargaining power between the households, the mayor and the firm.

## Trading & Micro structure “Focus on High Frequency Market Making”

**September 9th 2011, 9h30 – 12h30**

Collège de France – 3 rue d’Ulm – 75005 PARIS

The goal of the workshop is to be a forum for confronting viewpoints between practicioners and academics on topics related to developments in the area of market microstructure (limit order books, high frequency trading, optimal trading strategies, market design, competition between trading venues etc…). This is the 3rd edition of the worskhop.

## Optimal Portfolio Liquidation with Limit Orders

by **Olivier Guéant, Charles-Albert Lehalle & Joaquin Fernandez Tapia**

This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidity-consuming orders like Obizhaeva and Wang in [31], we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portfolio. Most practitioners address these two issues separately: they compute an optimal trading curve and they then send orders to the markets to try to follow it. The results obtained here solve simultaneously the two problems. As in a previous paper that solved the “intra-day market making problem” [19], the interactions of limit orders with the market are modeled via a Poisson process pegged to a diffusive “fair price” and a Hamilton-Jacobi-Bellman equation is used to solve the trade-off between execution risk and price risk. Backtests are finally carried out to exemplify the use of our results.

## Dealing with the Inventory Risk

by **Olivier Guéant**,** Charles-Albert Lehalle &** **Joaquin Fernandez Tapia**

Market makers have to continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency they indeed provide liquidity, is chal- lenged by the price risk they bear due to their inventory. In this paper, we provide optimal bid and ask quotes and closed-form approximations are derived using spectral arguments.

## From infinity to one: the reduction of some MFGs to planning problems

This paper presents recent results from Mean Field Game theory underlying the intro- duction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced in [11, 12, 13] and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation (see [14]), from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.

## Stochastic Target Problems with Controlled Loss in Jump Diffusion Models

By Ludovic Moreau Stochastic Target Problems with Controlled Loss in Jump Diffusion Models

In this paper, we consider a mixed diffusion version of the stochastic target problem introduced in [3]. This consists in finding the minimum initial value of a controlled process which guarantees to reach a controlled stochastic target with a given level of expected loss. As in [3], it can be converted into a standard stochastic target problem, as already studied in [10], [9] or [2] for the mixed diffusion case, by increasing both the state space and the dimension of the control. In our mixed-diffusion setting, the main difficulty comes from the presence of jumps, which leads to the introduction of a new kind of controls that take values in an unbounded set of measurable maps. This has non trivial technical impacts on the formulation and derivation of the associated partial differential equations.

Key words: Stochastic target problem, mixed diffusion process, discontinuous viscosity solu- tions, quantile hedging.

## Taux d’actualisation, modèles comptables et développement durable

**May 23, 24 and 25 2011 – Université Paris-Dauphine**

1ère séance (23/05),18h00 – 19h30, salle A707:

Conservation du capital : modèles comptables vs modèles financiers

2ème séance (24/05), 18h00 – 19h30, salle A707:

Actualisation et théorie économique : environmental economics vs ecological economics

3ème séance (25/05), 18h00 – 19h30, salle A707:

La comptabilité environnementale : une solution au problème de l’actualisation ?