An optimal trading problem in intraday electricity markets

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Table of contents

Résumé
Abstract
1 Introduction
1.1 Introduction
1.2 Première partie : estimation efficace dans un modèle à deux facteurs
1.3 Deuxième partie : estimation en présence d’erreurs de modèle
1.4 Troisième partie : exécution optimale sur le marché de l’électricité
1.5 Description des marchés de gros de l’électricité
1.6 Perspectives
2 Efficient estimation in a two-factor model from historical data
2.1 Introduction
2.1.1 Motivation
2.1.2 Setting
2.1.3 Main results and organization of the chapter
2.2 Construction of the estimators and convergence results
2.2.1 Rate-optimal estimation of #
2.2.2 Rate-optimal estimation of the volatility processes
2.2.3 Efficient estimation of # when d = 2
2.2.4 Discussion on the case d 3
2.3 Numerical implementation
2.3.1 Context of electricity forward contracts
2.3.2 Results on simulated data
2.3.3 Study based on real data from the French electricity market
2.4 Proofs
2.4.1 Preliminaries : localization
2.4.2 Proof of Theorem 2.1
2.4.3 Proof of Theorem 2.2
2.4.4 Proof of Theorem 2.3
2.4.5 Proof of Theorem 2.4
2.5 Appendices
2.5.1 Proof of Lemma 2.4.1
2.5.2 Technical lemmas
2.5.3 Some histograms from the numerical experiments
3 Estimation in a two-factor model incorporating model errors
3.1 Introduction
3.1.1 Motivation
3.1.2 Setting
3.1.3 Main results
3.2 Construction of the estimators and convergence results
3.2.1 Estimators of #
3.2.2 Nonparametric estimation of the volatility processes
3.2.3 Efficient estimation of # in presence of model errors, when d = 2
3.3 Numerical implementation
3.3.1 Results on real data
3.3.2 Experiment on model errors using simulated data
3.3.3 Impact of model errors on nonparametric estimation
3.4 Proofs
3.4.1 Preliminaries : localization
3.4.2 Proof of Theorem 3.1
3.4.3 Proof of Theorem 3.2
3.4.4 Proof of Theorem 3.3
3.4.5 Proof of Theorem 3.4
3.4.6 Proof of Theorem 3.5
3.4.7 Proof of Theorem 3.6
3.5 Appendices
3.5.1 Technical lemmas
3.5.2 Plots of nonparametric estimators with model errors
4 An optimal trading problem in intraday electricity markets
4.1 Introduction
4.2 Problem formulation
4.3 Optimal execution without delay in production
4.3.1 Auxiliary optimal execution problem
4.3.2 Approximate solution
4.3.3 Numerical results
4.4 Jumps in the residual demand forecast
4.4.1 Auxiliary optimal execution problem
4.4.2 Approximate solution
4.4.3 Numerical results
4.5 Delay in production
4.5.1 Explicit solution with delay
4.5.2 Numerical results
4.6 Appendices
4.6.1 Proof of Theorem 4.1
4.6.2 Proof of Theorem 4.2