This thesis deals with the stochastic optimization problem of hydro reservoir manage- ment. External inflows and market electricity price are both considered as random inputs to the model, which is designed as joint chance constrained programming. The main goal of the optimization problem is to maximize the profit from hydro energy usage together with minimizing the cost of used water. The random component is modelled by suitable stochastic processes based on historical data and then approximated via scenarios. Sea- sonal deterministic model is another model that is presented in this thesis. This model helps appraise water stored in every each reservoir's compartment. The estimates of water values are based on dual variables. Finally, in the practical part the hydro reservoir ma- nagement problem is applied to the real hydro valley located on the Vltava river. This part also deals with an option of increasing the number of pumping stations in this particular hydro valley.

Cette thèse étudie l’évolution des marchés du gaz naturel en Europe jusqu’en 2035 en utilisant les outils de la modélisation. Le modèle proposé, intitulé GaMMES, repose sur une description oligopolistique des marchés et ses principaux avantages sont les suivants : un niveau de détail important de la structure économique de la chaîne gazière et une prise en compte endogène des contrats de long-terme en amont ainsi que de la substitution avec les produits pétroliers et le charbon, au niveau de la demande. Dans un premier temps, nous étudions la question de la sécurité d’approvisionnement en gaz en Europe et les conditions favorables à la régulation des marchés vulnérables au risque de rupture d’approvisionnement, notamment de la part de la Russie. Trois études de cas sont proposées selon le degré de dépendance et la nature de régulation en place : le marché allemand des années 1980 et les marchés actuels de la Bulgarie et de l’Espagne. Nous étudions en particulier l’évolution des caractéristiques des marchés en fonction du risque de rupture et le type de régulation à mettre en place afin d’assurer l’optimalité du bien-être social. Ensuite, nous proposons un modèle de type systèmes dynamiques afin de prendre en compte la substitution énergétique entre le charbon, le pétrole et le gaz naturel. Notre approche permet d’estimer une nouvelle forme fonctionnelle de la fonction de demande pour le gaz naturel, qui englobe à la fois la substitution énergétique et les inerties de consommation dues aux investissements des usagers finaux. Dans un troisième temps, nous utilisons cette fonction de demande dans un modèle d’équilibre partiel des marchés du gaz naturel en Europe. Le modèle GaMMES, écrit sous forme de problème de complémentarité, représente les principaux acteurs de l’industrie du gaz naturel en considérant leurs interactions stratégiques et les pouvoirs de marchés. Il a été appliqué au marché du gaz naturel en Europe du nord-est afin d’étudier l’évolution, jusqu’en 2035, de la consommation, des prix spot, des prix et volumes long-terme, de la production et de la dépendance par rapport aux imports étrangers. Finalement, nous proposons une extension stochastique du modèle GaMMES afin d’analyser l’impact de la forte fluctuation du prix du Brent sur les marchés gaziers. Une étude économétrique a été menée afin de calculer la loi de probabilité du prix du pétrole, lorsqu’il est modélisé en tant que variable aléatoire, dans le but de construire et pondérer l’arbre des scénarii. Les résultats permettent de comprendre comment l’aléa modifie les comportements stratégiques des acteurs, notamment au niveau des contrats de long-terme. Enfin, la valeur de la solution stochastique est calculée afin de quantifier l’importance de la prise en compte des fluctuations du prix du pétrole pour chaque acteur de la chaîne. / This thesis studies the evolution of the natural gas markets in Europe, until 2035, using optimization theory tools. The model we develop, named GaMMES, is based on an oligopolistic description of the markets. Its main advantages are the following: we consider an important level of detail in the economic structure of the gas chain and we endogenously take into account long-term contracts in the upstream as well as energy substitution between gas, oil, and coal in the demand. In the first part of this thesis, we study the issue of security of supply in Europe and the conditions under which it is necessary to regulate the gas markets that are strongly dependent on foreign imports. Three case studies are then presented, regarding the level of dependence and the markets' specificities: the German gas trade of the 1980s and the current Spanish and Bulgarian markets. We study in particular the evolution of the markets' outcome as a function of the supply disruption probability and the kind of regulation to implement in order to maximize the social welfare. In the second part, we develop a system dynamics model in order to capture fuel substitution between oil, coal, and natural gas. Our approach allows one to calculate a new functional form of the demand function for natural gas that contains energy substitution and consumption inertia effects due to end-users' investments. In the third part, we take advantage of our demand function and use it in a partial equilibrium model of natural gas markets in Europe. The GaMMES model, when written as a complementarity problem, describes the principal gas chain actors as well as their strategic interactions and market power. It was applied to the northwestern European gas trade to analyze the evolution of consumption, spot and long-term contract prices and volumes, production, and natural gas dependence, until 2035. In the last part, we present a stochastic extension of the GaMMES model in order to study the impact of the strong Brent price fluctuation on the gas markets. An econometric analysis allowed us to calculate the probability law of the oil price, when taken as a random variable, in order to construct the scenario tree and estimate its weights. Our results show how uncertainty changes the strategic behavior, in particular for the long-term contracting activity. Finally, the value of the stochastic solution is calculated to quantify the importance of taking into account randomness in the optimization programs of the gas chain actors.

The common theme throughout the thesis is to explore the possibility of using a single framework, namely the systems theory framework, in modeling a few stylized features of a financial market. A systems theoretic model is developed, in this thesis in Chapter 3, for confidence bias of an individual. The effect of this bias on his investment decision is brought out explicitly. The phenomenon of excessive trading, arising due to overconfidence and optimism, has been explained. The concept of virtual capital, incorporating the ideas from prospect theory, is introduced. We have proposed a dynamical system framework to model limits to arbitrage and the herding behavior in financial markets in Chapter 4. The market evolves due to the participation of traders. It is instructive to look at the market as a system evolving from a set of initial conditions during every time interval. In the proposed model, herding is defined as a specific relation between the system responses. The proposed herding measure quantifies how far the individual is from clustering with others. It is also shown how this interpretation helps us to understand the effects of herding. There exists a risk when the market price variation, due to herding, is thought of as entirely due to the portfolio fundamentals. The generic dynamical system model that captures some aspects of the limits of arbitrage is also proposed wherein fundamental risk, noise trader risk, implementation risk, and model risk can be incorporated. The proposed model offers a single framework to study the Marginally Efficient Market and Synchronization Risk models. In Chapter 5, we have proposed a switching dynamical system with minority game rules incorporated within the framework. We have explored the possibility of developing a market model, in Chapter 6, in the same framework that has been used to develop models for arbitrage and herding. We have explored, in this thesis, the possibility of using a single framework to model stylized features of stock market. It will be a long way before a single model can capture all complex characteristic features of a stock market. We have attempted, in this thesis, to capture a few stylized features in a single framework, if not in a single model. Different models proposed for individual confidence bias, limits to arbitrage, herding, and switching model for incorporating minority games are all set up in system dynamics framework. This leads to a stage where one can explore incorporating other features, not addressed in this thesis, in system dynamics framework. If each feature is captured using a different framework like confidence bias as stochastic system, herding as pattern cluster, limits to arbitrage as rule-based agents, etc., it would be difficult to integrate them into a single framework. But, in the present work, we have captured the chosen stylized features using system dynamics framework though individual models differ from each other substantially. The challenges are many in creating a single framework. The vision of such framework may involve different components such as modeling decision making, considering risk profiles, devising investment strategies, etc. Stylized features would come as emergent properties of complex interactions among the components of the system. Emergence refers to the way in which multiplicity of simple interactions lead to complex behavior. Emergence of such features may include different time scales of causal relationships among components. System may have thresholds, determined by diversity of traders and nature of interactions, which is vital for features to become emergent. This can be seen in practice. Stock market regulates the relative prices of companies across the world. There is no single central agency to control the workings of the market. Traders have knowledge of only few companies within their portfolio, and to follow transaction rules. Trends and patterns are still emerging which are studied by technical analysts. Emergent properties are mostly signature of self-organizing complex system. Self-organization in complex system relies on four properties which are fundamental in system dynamics framework: positive feedback, negative feedback, multiple interactions, and balance among strategies. A complex adaptive stock market system which is self-organizing and exhibit stylized features as emergent property is a distant goal of system theorists around the world. The challenge does not end there. We have attempted to model and study the stylized features of a stock market in systems theory framework. The focus of our approach is to use the dynamical system modeling to study the features. We have not considered the investment aspects in a financial market. The investment models are very important in real life for individuals and policy-makers. Future extension of the ideas explored in this thesis could be along the lines of creating investment models for individuals and policy-makers. Creating such models using complex adaptive stock market system goes a long way in understanding a phenomenon that had started by Dutch East India Company issuing shares on Amsterdam Stock Exchange way back in 1602.