41 research outputs found
An adverse selection approach to power pricing
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 problems 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 for the problem at hand. The optimal contracts are either
linear or polynomial with respect to the consumption. Whenever the outside
options offered by competitors are not uniform among the different type of
consumers, we exhibit situations where the electricity provider should contract
with consumers with either low or high appetite for electricity.Comment: 39 pages, 9 figure
A mean field model for the development of renewable capacities
We propose a model based on a large number of small competitive producers of
renewable energies, to study the effect of subventions on the aggregate level
of capacity, taking into account a cannibalization effect. We first derive a
model to explain how long-time equilibrium can be reached on the market of
production of renewable electricity and compare this equilibrium to the case of
monopoly. Then we consider the case in which other capacities of production
adjust to the production of renewable energies. The analysis is based on a
master equation and we get explicit formulae for the long-time equilibria. We
also provide new numerical methods to simulate the master equation and the
evolution of the capacities. Thus we find the optimal subventions to be given
by a central planner to the installation and the production in order to reach a
desired equilibrium capacity
A Rank-Based Reward between a Principal and a Field of Agents: Application to Energy Savings
We consider a problem where a Principal aims to design a reward function to a
field of heterogeneous agents. In our setting, the agents compete with each
other through their rank within the population in order to obtain the best
reward. We first explicit the equilibrium for the mean-field game played by the
agents, and then characterize the optimal reward in the homogeneous setting.
For the general case of a heterogeneous population, we develop a numerical
approach, which is then applied to the specific case study of the market of
Energy Saving Certificates
Expert Aggregation for Financial Forecasting
Machine learning algorithms dedicated to financial time series forecasting
have gained a lot of interest over the last few years. One difficulty lies in
the choice between several algorithms, as their estimation accuracy may be
unstable through time. In this paper, we propose to apply an online
aggregation-based forecasting model combining several machine learning
techniques to build a portfolio which dynamically adapts itself to market
conditions. We apply this aggregation technique to the construction of a
long-short-portfolio of individual stocks ranked on their financial
characteristics and we demonstrate how aggregation outperforms single
algorithms both in terms of performances and of stability
Two approaches for effective modelling of rain-rate time-series for radiocommunication system simulations
The paper presents a model which allows to synthetically generate rain rate time-series for a fixed location. Rain rate time-series are very much correlated with signal attenuation in Ka band and above and, thus, enable to realistically simulate propagation effects on Earth-satellite links. The model presented are based on Markov chains
Ergodic control of a heterogeneous population and application to electricity pricing
We consider a control problem for a heterogeneous population composed of
customers able to switch at any time between different contracts, depending not
only on the tariff conditions but also on the characteristics of each
individual. A provider aims to maximize an average gain per time unit,
supposing that the population is of infinite size. This leads to an ergodic
control problem for a "mean-field" MDP in which the state space is a product of
simplices, and the population evolves according to a controlled linear
dynamics. By exploiting contraction properties of the dynamics in Hilbert's
projective metric, we show that the ergodic eigenproblem admits a solution.
This allows us to obtain optimal strategies, and to quantify the gap between
steady-state strategies and optimal ones. We illustrate this approach on
examples from electricity pricing, and show in particular that the optimal
policies may be cyclic-alternating between discount and profit taking stages
Quadratic Regularization of Unit-Demand Envy-Free Pricing Problems and Application to Electricity Markets
We consider a profit-maximizing model for pricing contracts as an extension
of the unit-demand envy-free pricing problem: customers aim to choose a
contract maximizing their utility based on a reservation bill and multiple
price coefficients (attributes). A classical approach supposes that the
customers have deterministic utilities; then, the response of each customer is
highly sensitive to price since it concentrates on the best offer. A second
approach is to consider logit model to add a probabilistic behavior in the
customers' choices. To circumvent the intrinsic instability of the former and
the resolution difficulties of the latter, we introduce a quadratically
regularized model of customer's response, which leads to a quadratic program
under complementarity constraints (QPCC). This allows to robustify the
deterministic model, while keeping a strong geometrical structure. In
particular, we show that the customer's response is governed by a polyhedral
complex, in which every polyhedral cell determines a set of contracts which is
effectively chosen. Moreover, the deterministic model is recovered as a limit
case of the regularized one. We exploit these geometrical properties to develop
an efficient pivoting heuristic, which we compare with implicit or non-linear
methods from bilevel programming. These results are illustrated by an
application to the optimal pricing of electricity contracts on the French
market.Comment: 37 pages, 9 figures; adding a section on the pricing of electricity
contract