You are previewing Optimization Methods in Finance.
O'Reilly logo
Optimization Methods in Finance

Book Description

Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Dedication
  6. Contents
  7. Foreword
  8. 1. Introduction
    1. 1.1 Optimization problems
    2. 1.2 Optimization with data uncertainty
    3. 1.3 Financial mathematics
  9. 2. Linear programming: theory and algorithms
    1. 2.1 The linear programming problem
    2. 2.2 Duality
    3. 2.3 Optimality conditions
    4. 2.4 The simplex method
  10. 3. LP models: asset/liability cash-flow matching
    1. 3.1 Short-term financing
    2. 3.2 Dedication
    3. 3.3 Sensitivity analysis for linear programming
    4. 3.4 Case study: constructing a dedicated portfolio
  11. 4. LP models: asset pricing and arbitrage
    1. 4.1 Derivative securities and fundamental theorem of asset pricing
    2. 4.2 Arbitrage detection using linear programming
    3. 4.3 Additional exercises
    4. 4.4 Case study: tax clientele effects in bond portfolio management
  12. 5. Nonlinear programming: theory and algorithms
    1. 5.1 Introduction
    2. 5.2 Software
    3. 5.3 Univariate optimization
    4. 5.4 Unconstrained optimization
    5. 5.5 Constrained optimization
    6. 5.6 Nonsmooth optimization: subgradient methods
  13. 6. NLP models: volatility estimation
    1. 6.1 Volatility estimation with GARCH models
    2. 6.2 Estimating a volatility surface
  14. 7. Quadratic programming: theory and algorithms
    1. 7.1 The quadratic programming problem
    2. 7.2 Optimality conditions
    3. 7.3 Interior-point methods
    4. 7.4 QP software
    5. 7.5 Additional exercises
  15. 8. QP models: portfolio optimization
    1. 8.1 Mean-variance optimization
    2. 8.2 Maximizing the Sharpe ratio
    3. 8.3 Returns-based style analysis
    4. 8.4 Recovering risk-neural probabilities from options prices
    5. 8.5 Additional exercises
    6. 8.6 Case study: constructing an efficient portfolio
  16. 9. Conic optimization tools
    1. 9.1 Introduction
    2. 9.2 Second-order cone programming
    3. 9.3 Semidefinite programming
    4. 9.4 Algorithms and software
  17. 10. Conic optimization models in finance
    1. 10.1 Tracking error and volatility constraints
    2. 10.2 Approximating covariance matrices
    3. 10.3 Recovering risk-neutral probabilities from options prices
    4. 10.4 Arbitrage bounds for forward start options
  18. 11. Integer programming: theory and algorithms
    1. 11.1 Introduction
    2. 11.2 Modeling logical conditions
    3. 11.3 Solving mixed integer linear programs
  19. 12. Integer programming models: constructing an index fund
    1. 12.1 Combinatorial auctions
    2. 12.2 The lockbox problem
    3. 12.3 Constructing an index fund
    4. 12.4 Portfolio optimization with minimum transaction levels
    5. 12.5 Additional exercises
    6. 12.6 Case study: constructing an index fund
  20. 13. Dynamic programming methods
    1. 13.1 Introduction
    2. 13.2 Abstraction of the dynamic programming approach
    3. 13.3 The knapsack problem
    4. 13.4 Stochastic dynamic programming
  21. 14. DP models: option pricing
    1. 14.1 A model for American options
    2. 14.2 Binomial lattice
  22. 15. DP models: structuring asset-backed securities
    1. 15.1 Data
    2. 15.2 Enumerating possible tranches
    3. 15.3 A dynamic programming approach
    4. 15.4 Case study: structuring CMOs
  23. 16. Stochastic programming: theory and algorithms
    1. 16.1 Introduction
    2. 16.2 Two-stage problems with recourse
    3. 16.3 Multi-stage problems
    4. 16.4 Decomposition
    5. 16.5 Scenario generation
  24. 17. Stochastic programming models: Value-at-Risk and Conditional Value-at-Risk
    1. 17.1 Risk measures
    2. 17.2 Minimizing CVaR
    3. 17.3 Example: bond portfolio optimization
  25. 18. Stochastic programming models: asset/liability management
    1. 18.1 Asset/liability management
    2. 18.2 Synthetic options
    3. 18.3 Case study: option pricing with transaction costs
  26. 19. Robust optimization: theory and tools
    1. 19.1 Introduction to robust optimization
    2. 19.2 Uncertainty sets
    3. 19.3 Different flavors of robustness
    4. 19.4 Tools and strategies for robust optimization
  27. 20. Robust optimization models in finance
    1. 20.1 Robust multi-period portfolio selection
    2. 20.2 Robust profit opportunities in risky portfolios
    3. 20.3 Robust portfolio selection
    4. 20.4 Relative robustness in portfolio selection
    5. 20.5 Moment bounds for option prices
    6. 20.6 Additional exercises
  28. Appendix A Convexity
  29. Appendix B Cones
  30. Appendix C A probability primer
  31. Appendix D The revised simplex method
  32. References
  33. Index