Ergodic control of a heterogeneous population and application to electricity pricing - Q. Jacquet, W. van Ackooij, C. Alasseur & S. Gaubert

We consider a dynamic pricing model, in which a population of customers can change contracts at any time depending on pricing conditions and customer-specific characteristics such as inertia (propensity to stay with the same supplier). A supplier then seeks to maximise its average revenue per unit time, assuming that the population is of infinite size (the 'mean field' limit). We present an application to energy pricing, and solve this problem by applying an iteration algorithm on relative values. Read more [...]


Day-ahead probabilistic forecast of solar irradiance: a Stochastic Differential Equation approach - J. Badosa, E. Gobet, M. Grangereau and D. Kim

In this work, we derive a probabilistic forecast of the solar irradiance during a day at a given location, using a stochastic differential equation (SDE for short) model. We propose a procedure that transforms a deterministic forecast into a probabilistic forecast: the input parameters of the SDE model are the AROME numerical weather predictions computed at day D-1 for the day D. The model also accounts for the maximal irradiance from the clear sky model. The SDE model is mean-reverting towards Read more [...]



We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We build on the mathematical model introduced in [14] and optimize the diesel con-sumption under a “no-blackout” constraint. We introduce a methodology to solve microgrid man-agement problem using different variants of Read more [...]


Variance optimal hedging with application to Electricity markets - Xavier Warin

In this article, we use the mean variance hedging criterion to value contracts in incomplete markets. Although the problem is well studied in a continuous and even discrete framework, very few works incorporating illiquidity constraints have been achieved and no algorithm is available in the literature to solve this problem. We first show that the valuation problem incorporating illiquidity constraints with a mean variance criterion admits a unique solution. Then we develop two Least Squares Read more [...]


Estimating fast mean-reverting jumps in electricity Market models - Thomas Deschatre, Olivier Féron, and Marc Hoffmann

Based on empirical evidence of fast mean-reverting spikes, we model electricity price processes as the sum of a continuous Itö semimartingale and a a mean-reverting compound Poisson process. In a first part, we investigate the estimation of the two parameters of the Poisson process from discrete observations and establish asymptotic efficiency in various asymptotic settings. In a second part, we discuss the use of our inference results for correcting the value of forward contracts on electricity Read more [...]


t and stable multivariate kernel density estimation by fast sum updating - N . Langrené, X. Warin

Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at M evaluation points given N input sample points requires a quadratic O(MN) operations, which is prohibitive for large scale problems. For this reason, approximate methods such as binning with Fast Fourier Transform or the Fast Gauss Transform have been proposed to speed up kernel density estimation. Among these fast methods, the Fast Sum Updating Read more [...]


Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEs - X. Warin

We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not su er from the so called curse of dimensionality and it can be used to solve problems that were out of reach so far. We give some results of convergence and show numerically that it is effective. Besides we numerically show that the new scheme developed can be used to solve some full non linear PDEs. At last we provide an effective algorithm to implement Read more [...]


Option valuation and hedging using asymmetric risk function: asymptotic optimality through fully nonlinear Partial Differential Equations - Emmanuel Gobet, Isaque Pimentel, Xavier Warin

Discrete time hedging produces a residual risk, namely, the tracking error. The major problem is to get valuation/hedging policies minimizing this error. We evaluate the risk between trading dates through a function penalizing asymmetrically profits and losses. After deriving the asymptotics within a discrete time risk measurement for a large number of trading dates, we derive the optimal strategies minimizing the asymptotic risk in the continuous time setting. We characterize the optimality through Read more [...]


Nesting Monte Carlo for high-dimensional Non Linear PDEs - Xavier Warin

A new method based on nesting Monte Carlo is developed to solve highdimensional semi-linear PDEs. Convergence of the method is proved and its convergence rate studied. Results in high dimension for different kind of non-linearities show its efficiency.


Assessing the implementation of the Market Stability Reserve

Corinne Chaton, Anna Creti, and Maria-Eugenia Sanin, Abstract In October 2015 the European Parliament has established a market stability reserve (MSR) in the Phase 4 of the EU-ETS, as part of the 2030 framework for climate policies. In this paper we model the EU-ETS in presence of the Market Stability Reserve (MSR) as it is de ned by that decision and investigate the impact that such a measure has in terms of permits price, output production and banking strategies. To do so we build an inter-temporal Read more [...]

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