Archives

1
Nov

A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs

Arash Fahim, Nizar Touzi, Xavier Warin We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in [10], and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretization error in terms of the time step. An explicit implementable scheme Read more [...]

1
Oct

Market Design for Emission Trading Schemes

René Carmona, Max Fehr, Juri Hinz, Arnaud Porchet This paper is concerned with the mathematical analysis of emissions markets. We review the existing quantitative analyses on the subject and introduce some of the mathematical challenges posed by the implementation of the new phase of the European Union Emissions Trading Scheme as well as the cap-and-trade schemes touted by the US, Canada, Australia and Japan. From a practical point of view, the main thrust of the paper is the design and numerical Read more [...]

1
Sep

L2 Density Estimation Under Constraints

Christian Musso, Nadia Oudjane This paper presents a general methodology to estimate a probability density under linear constraints (on the support, bounded moments or quantiles,. . . ). The proposed approximation is the projection of the free density estimation on the set of the probability densities satisfying the constraints. In some cases, the solution of this projection problem can be expressed in a simple parametric form as a function of the free density estimate. Plus d'infos. Read more [...]

1
Jun

Valuation of a powerplant under production constraints and markets incompleteness

A. Porchet, N. Touzi, X. Warin Mathematical Methods of Operations research 70(1) pp 47-75 - Juin 2009 Plus d'infos.

1
Jun

A Structural Risk-Neutral Model of Electricity Prices

René Aïd, Luciano Campi, Adrien Nguyen Huu, Nizar Touzi The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying market of fuels, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the electricity spot prices depend on the dynamics of the electricity demand at the maturity T, and on the random available capacity of each production means. Read more [...]

1
May

Large Scale Experiment and Optimization of a Distributed Stochastic Control Algorithm. Application to Energy Management Problems

P. Vezolle, S.Vialle, X.Warin Large-Scale Parallel Processing 2009 Mai 2009 Plus d'infos.

1
Feb

Hedging and Vertical Integration in Electricity Markets

René Aïd, Gilles Chemla, Arnaud Porchet, Nizar Touzi This paper analyzes the interactions between vertical integration and (wholesale) spot, forward and retail markets in risk management. We develop an equilibrium model that fits electricity markets well. We point out that vertical integration and forward hedging are two separate levers for demand and spot price risk diversification. We show that they are imperfect substitutes as to their impact on retail prices and agents’ utility because the Read more [...]

1
Jan

Storage and Security of Supply in the Medium Run

C. Chaton, A. Creti, B. Villeneuve Resource & Energy Economics 31(1), pp 24-38 - Janvier 2009 Plus d'infos.

1
Jan

Optimal transportation and the falsifiability of incompletely specified economic models

I. Ekeland, A. Galichon, M. Henry Economic Theory 42(2) pp. 355-374 - Janvier 2009 Plus d'infos.

1
Dec

Long-Term Risk Management for Utility Companies: the Next Challenges

René Aïd Since the energy markets liberalisation at the beginning of the 1990s in Europe, electricity monopolies have gone through a profound evolution process. From an industrial organisation point of view, they lost their monopoly on their historical business, but gained the capacity to develop in any sector. Companies went public and had to upgrade their financial risk management process to international standards and implement modern risk management concepts and reporting processes (VaR, EaR...). Read more [...]

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