An Adverse Selection Approach to Power Tarification

Clémence Alasseur, Ivar Ekeland, Romuald Élie, Nicolás Hernández Santibáñez and Dylan Possamaï We study the optimal design of electricity contracts among a population of consumers with different needs. This question is tackled within the framework of Principal-Agent problem in presence of adverse selection. The particular features of electricity induce an unusual structure on the production cost, with no decreasing return to scale. We are nevertheless able to provide an explicit solution Read more [...]


StOpt library

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Capacity Expansion Games with Application to Competition in Power Generation Investments

R. Aid, L. Li, M. Ludkovski We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically uctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing strategies characterized through threshold rules. Because the impact of changing costs on the producers is asymmetric, we are led to a nonzerosum timing game describing the transitions among the discrete investment stages. Read more [...]


The financialization of the term structure of risk premia in commodity markets

Edouard Jaeck In this paper, I examine how financialization affects the term structure of risk premia by using an equilibrium model for commodity futures markets. I define financialization as the entry of cross-asset investors, who are exposed to a commodity risk, into a commodity market. Qualitatively, the model shows that the financialization decreases the segmentation between commodity markets and the stock market. It also shows that speculators and investors both provide and consume liquidity Read more [...]


Unbiased Monte Carlo estimate of stochastic differential equations expectations

Mahamadou Doumbia, Nadia Oudjane,  Xavier Warin  We propose an unbiased Monte Carlo method to compute E(g(XT ))  where g is a Lipschitz function and X an Ito process. This approach extends the method proposed in [16] to the case where X is solution of a multidimensional stochastic differential equation with varying drift and diffusion coefficients. A variance reduction method relying on interacting particle systems is also developed. Key words: unbiased estimate, linear parabolic PDEs, interacting Read more [...]


Contracting theory with competitive interacting Agents

Romuald Elie  Dylan Possamaï In a framework close to the one developed by Holmstrom and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, as wel las impact (positively or negatively) the projects of the other Agents. Considering economic agents in competition with relative performance concerns, we derive the optimal contracts in both first best and moral Read more [...]


A Non-Intrusive Stratified Resampler for Regression Monte Carlo: Application to Solving Non-Linear Equations

EMMANUEL GOBET, GANG LIU, AND JORGE P. ZUBELLI Abstract. Our goal is to solve certain dynamic programming equations associated to a given Markov chain X, using a regression-based Monte Carlo algorithm. More speci cally, we assume that the model for X is not known in full detail and only a root sample X1; : : : ;XM of such process is available. By a strati cation of the space and a suitable choice of a probability measure , we design a new resampling scheme that allows to compute local regressions Read more [...]


Pricing American options using martingale bases

J. Lelong In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers [2002]. Our approach relies on approximating the set of uniformly square integrable martingales by a finite dimensional Wiener chaos expansion. Then, we use a sample average approximation technique to efficiently solve the optimization problem. Unlike all the regression based methods, our method can transparently deal with path dependent options Read more [...]


Volatility in electricity derivative markets: the Samuelson effect revisited

Edouard Jaeck, Delphine Lautier This article proposes an empirical study of the Samuelson effect in electricity markets. Our motivations are twofold. First, although the literature largely assesses the decreasing pattern in the volatilities along the price curve in commodity markets, it has not extensively tested the presence of such a dynamic feature in electricity prices. Second, the analysis of a non-storable commodity enriches the literature on the behavior of commodity prices. Indeed, Read more [...]


Forward Feynman-Kac Type Representation for Semilinear Nonconservative Partial Differential Equations

Anthony LE CAVIL, Nadia OUDJANE and Francesco RUSSO We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness in the first part of the article. The second part is devoted to the construction of a probabilistic particle algorithm and the proof of its convergence. Illustrations of the efficiency of the algorithm are provided by numerical experiments. Read more [...]

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