Description
Book Synopsis1. Optimization in Energy Markets
1.1 Classification of optimization problems
1.1.1 Linear versus Nonlinear Problems
1.1.2 Deterministic versus Stochastic Problems
1.1.3 Static versus Dynamic Problems
1.2 Optimal portfolio selection among different investment alternatives
1.3 Energy Asset Optimization
1.3.1 Generation Asset Investment Valuation with Real Option Methodology
1.3.2 Generation, Transportation and Storage Asset Operational Optimization and Valuation
1.4 Energy Trading and Optimization
1.4.1 Asset allocation with Capital Constraints
1.4.2 Intraday trading
2. Optimization Methods
2.1 Linear Optimization
2.1.1 LP problems
2.2 Nonlinear Optimization
2.2.1 Unconstrained problem
2.2.2 Constrained Problems with Equality Constraints
2.2.3 Constrained Problems with Inequalities Constraints
2.3 Pricing financial assets
2.3.1 Pricing in energy markets
2.3.2 Pricing in incomplete markets
2.3.3 A motivating examp
Trade ReviewEnergy markets are extremely competitive markets. Optimization of business decisions is fundamental for performance maximization. This book represents an excellent synthesis of optimization theory and practice applied to a wide and significant range of cutting-edge business problems characterizing power and natural gas markets.'
- Domenico De Luca, CEO, Axpo Trading and Member of Executive Board Axpo Group
'Optimization methods play an important role when making decisions and managing risk in today's liberalized energy markets. When planning a power plant or entering a structured gas contract, stochastic control is the key mathematical tool to assess the inherent risk. The authors of this book present an excellent account of the problems and methods for optimization in energy and power markets. The scope ranges from a rigorous theoretical analysis of the control problems, through numerical methods and to in-depth discussions of relevant practical case studies. This book is unique in providing a solid mathematical analysis of various optimization problems, yet never losing the market practice out of sight. It will be an invaluable reference for both academics and practitioners in power and gas markets.'
- Fred Espen Benth, Professor of Mathematical Finance at the University of Oslo, Department of Mathematics and Deputy Manager
Table of Contents1. Optimization in Energy Markets
1.1 Classification of optimization problems
1.1.1 Linear versus Nonlinear Problems
1.1.2 Deterministic versus Stochastic Problems
1.1.3 Static versus Dynamic Problems
1.2 Optimal portfolio selection among different investment alternatives
1.3 Energy Asset Optimization
1.3.1 Generation Asset Investment Valuation with Real Option Methodology
1.3.2 Generation, Transportation and Storage Asset Operational Optimization and Valuation
1.4 Energy Trading and Optimization
1.4.1 Asset allocation with Capital Constraints
1.4.2 Intraday trading
2. Optimization Methods
2.1 Linear Optimization
2.1.1 LP problems
2.2 Nonlinear Optimization
2.2.1 Unconstrained problem
2.2.2 Constrained Problems with Equality Constraints
2.2.3 Constrained Problems with Inequalities Constraints
2.3 Pricing financial assets
2.3.1 Pricing in energy markets
2.3.2 Pricing in incomplete markets
2.3.3 A motivating example: utility indifference pricing
2.4 Deterministic Dynamic Programming
2.5 Stochastic Dynamic Programming, discrete time
2.5.1 A motivating example
2.5.2 The general case
2.5.3 Tree methods
2.5.4 Least Square Monte Carlo methods
2.5.5 Naïve Monte Carlo with Linear Programming
2.6 Stochastic Dynamic Programming, continuous time
2.6.1 The Hamilton-Jacobi-Bellman equation
2.7 Deterministic numerical methods
2.7.1 Finite Difference Method for HJB equation
2.7.2 Boundary conditions
2.8 Probabilistic numerical methods
2.8.1 Tree methods, continuous time
2.8.2 Computationally simple trees in dimension 1
2.8.3 Lattice of trees
2.8.4 Monte Carlo methods
3. Cases on Static Optimization
3.1 Case A: investment alternatives
3.2 Case B: Optimal generation mix for an electricity producer: a mean-variance approach
3.3 Conclusions
4. Valuing project's exibilities using the diagrammatic approach
4.1 Introduction
4.2 Description of the Investment Problem
4.3 Traditional evaluation Methods
4.4 Modelling Electricity Price Dynamics
4.5 Valuing Investment Flexibilities By Means Of The Lattice Approach
4.5.1 Investment alternative A
4.5.2 Investment alternative B
4.5.3 Investment alternative C
4.6 Conclusions
5. Virtual Power Plant Contracts
5.1 Introduction
5.2 Valuation Problem
5.2.1 Example
6. Algorithms comparison
The Swing Case
6.1 Introduction
6.2 Swing contracts
6.2.1 Indexed strike price modelling for gas swing contracts
6.2.2 The stochastic control problem
6.2.3 Dynamic Programming
6.3 Finite difference algorithm
6.3.1 Boundary conditions
6.3.2 The algorithm
6.4 Least Square Monte Carlo algorithm
6.4.1 The algorithm, and a reduction to one dimension
6.5 Naïve Monte Carlo with Linear Programming
6.6 Numerical Experiments
6.6.1 Finite differences
6.6.2 Least Square Monte Carlo
6.6.3 One year contract
6.7 Conclusions
7. Storage contracts
7.1 The contract
7.2 The evaluation problem
7.3 The optimal strategy (in the case of a physical gas storage)
7.4 The implementation
7.4.1 The gas cave
7.4.2 The gas spot price
7.4.3 The boundary conditions
7.4.4 Numerical experiment, no-penalty case
7.4.5 Numerical experiment, penalty case
8. Optimal Trading Strategies in Intraday Power Markets
8.1 Intraday power markets
8.1.1 Intraday power price features
8.1.2 Conclusions
8.2 Optimal Algorithmic Trading in Auction-Based Intraday Power Markets
8.2.1 The optimization problem
8.2.2 Example: Italian intra-day market
8.3 Optimal Algorithmic Trading in Continuous Time Power Markets
8.3.1 The optimization problem
8.3.2 Example: EPEX Spot market
