Optimization Methods in Finance Mathematics Finance and Risk Book 5 1st edition by Gerard Cornuejols, Reha Tütüncü ISBN 978-0521861700
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ISBN 13: 978-0521861700
Author: Gerard Cornuejols, Reha Tütüncü
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.
Optimization Methods in Finance (Mathematics Finance and Risk Book 5) 1st Table of contents:
1. Introduction
1.1 Optimization problems
1.2 Optimization with data uncertainty
1.3 Financial mathematics
2. Linear programming: theory and algorithms
2.1 The linear programming problem
2.2 Duality
2.3 Optimality conditions
2.4 The simplex method
3. LP models: asset/liability cash-flow matching
3.1 Short-term financing
3.2 Dedication
3.3 Sensitivity analysis for linear programming
3.4 Case study: constructing a dedicated portfolio
4. LP models: asset pricing and arbitrage
4.1 Derivative securities and fundamental theorem of asset pricing
4.2 Arbitrage detection using linear programming
4.3 Additional exercises
4.4 Case study: tax clientele effects in bond portfolio management
5. Nonlinear programming: theory and algorithms
5.1 Introduction
5.2 Software
5.3 Univariate optimization
5.4 Unconstrained optimization
5.5 Constrained optimization
5.6 Nonsmooth optimization: subgradient methods
6. NLP models: volatility estimation
6.1 Volatility estimation with GARCH models
6.2 Estimating a volatility surface
7. Quadratic programming: theory and algorithms
7.1 The quadratic programming problem
7.2 Optimality conditions
7.3 Interior-point methods
7.4 QP software
7.5 Additional exercises
8. QP models: portfolio optimization
8.1 Mean-variance optimization
8.2 Maximizing the Sharpe ratio
8.3 Returns-based style analysis
8.4 Recovering risk-neural probabilities from options prices
8.5 Additional exercises
8.6 Case study: constructing an efficient portfolio
9. Conic optimization tools
9.1 Introduction
9.2 Second-order cone programming
9.3 Semidefinite programming
9.4 Algorithms and software
10. Conic optimization models in finance
10.1 Tracking error and volatility constraints
10.2 Approximating covariance matrices
10.3 Recovering risk-neutral probabilities from options prices
10.4 Arbitrage bounds for forward start options
11. Integer programming: theory and algorithms
11.1 Introduction
11.2 Modeling logical conditions
11.3 Solving mixed integer linear programs
12. Integer programming models: constructing an index fund
12.1 Combinatorial auctions
12.2 The lockbox problem
12.3 Constructing an index fund
12.4 Portfolio optimization with minimum transaction levels
12.5 Additional exercises
12.6 Case study: constructing an index fund
13. Dynamic programming methods
13.1 Introduction
13.2 Abstraction of the dynamic programming approach
13.3 The knapsack problem
13.4 Stochastic dynamic programming
14. DP models: option pricing
14.1 A model for American options
14.2 Binomial lattice
15. DP models: structuring asset-backed securities
15.1 Data
15.2 Enumerating possible tranches
15.3 A dynamic programming approach
15.4 Case study: structuring CMOs
16. Stochastic programming: theory and algorithms
16.1 Introduction
16.2 Two-stage problems with recourse
16.3 Multi-stage problems
16.4 Decomposition
16.5 Scenario generation
17. Stochastic programming models: Value-at-Risk and Conditional Value-at-Risk
17.1 Risk measures
17.2 Minimizing CVaR
17.3 Example: bond portfolio optimization
18. Stochastic programming models: asset/liability management
18.1 Asset/liability management
18.2 Synthetic options
18.3 Case study: option pricing with transaction costs
19. Robust optimization: theory and tools
19.1 Introduction to robust optimization
19.2 Uncertainty sets
19.3 Different flavors of robustness
19.4 Tools and strategies for robust optimization
20. Robust optimization models in finance
20.1 Robust multi-period portfolio selection
20.2 Robust profit opportunities in risky portfolios
20.3 Robust portfolio selection
20.4 Relative robustness in portfolio selection
20.5 Moment bounds for option prices
20.6 Additional exercises
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Gerard Cornuejols,Reha Tütüncü,Optimization Methods,Mathematics Finance
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