14,063 research outputs found
Wind-pv-thermal power aggregator in electricity market
This paper addresses the aggregation of wind, photovoltaic and thermal units with the aim to improve bidding in an electricity market. Market prices, wind and photovoltaic powers are assumed as data given by a set of scenarios. Thermal unit modeling includes start-up costs, variables costs and bounds due to constraints of technical operation, such as: ramp up/down limits and minimum up/down time limits. The modeling is carried out in order to develop a mathematical programming problem based in a stochastic programming approach formulated as a mixed integer linear programming problem. A case study comparison between disaggregated and aggregated bids for the electricity market of the Iberian Peninsula is presented to reveal the advantage of the aggregation
Robust risk aggregation with neural networks
We consider settings in which the distribution of a multivariate random
variable is partly ambiguous. We assume the ambiguity lies on the level of the
dependence structure, and that the marginal distributions are known.
Furthermore, a current best guess for the distribution, called reference
measure, is available. We work with the set of distributions that are both
close to the given reference measure in a transportation distance (e.g. the
Wasserstein distance), and additionally have the correct marginal structure.
The goal is to find upper and lower bounds for integrals of interest with
respect to distributions in this set. The described problem appears naturally
in the context of risk aggregation. When aggregating different risks, the
marginal distributions of these risks are known and the task is to quantify
their joint effect on a given system. This is typically done by applying a
meaningful risk measure to the sum of the individual risks. For this purpose,
the stochastic interdependencies between the risks need to be specified. In
practice the models of this dependence structure are however subject to
relatively high model ambiguity. The contribution of this paper is twofold:
Firstly, we derive a dual representation of the considered problem and prove
that strong duality holds. Secondly, we propose a generally applicable and
computationally feasible method, which relies on neural networks, in order to
numerically solve the derived dual problem. The latter method is tested on a
number of toy examples, before it is finally applied to perform robust risk
aggregation in a real world instance.Comment: Revised version. Accepted for publication in "Mathematical Finance
Learning by mirror averaging
Given a finite collection of estimators or classifiers, we study the problem
of model selection type aggregation, that is, we construct a new estimator or
classifier, called aggregate, which is nearly as good as the best among them
with respect to a given risk criterion. We define our aggregate by a simple
recursive procedure which solves an auxiliary stochastic linear programming
problem related to the original nonlinear one and constitutes a special case of
the mirror averaging algorithm. We show that the aggregate satisfies sharp
oracle inequalities under some general assumptions. The results are applied to
several problems including regression, classification and density estimation.Comment: Published in at http://dx.doi.org/10.1214/07-AOS546 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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