Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean–variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean–variance optimization, multi-period models, and additional material to highlight the relevance to finance. -- Read more...
Abstract:
This is a thorough treatment of optimization techniques that solve central challenges in finance. It gives a complete picture of model formulation, gathering relevant data, and computational implementation for each problem discussed. Theory and practical applications are woven together and enriched with worked examples, exercises, and case studies. Read more...
Author(s): Cornuejols, Gerard; Peña, Javier Francisco; Tütüncü, Reha
Edition: Second edition
Publisher: Cambridge University Press
Year: 2018
Language: English
Pages: 337
Tags: Finance -- Mathematical models.;Mathematical optimization.
Content: Machine generated contents note: 1.Overview of Optimization Models --
1.1.Types of Optimization Models --
1.2.Solution to Optimization Problems --
1.3.Financial Optimization Models --
1.4.Notes --
2.Linear Programming: Theory and Algorithms --
2.1.Linear Programming --
2.2.Graphical Interpretation of a Two-Variable Example --
2.3.Numerical Linear Programming Solvers --
2.4.Sensitivity Analysis --
2.5.*Duality --
2.6.*Optimality Conditions --
2.7.*Algorithms for Linear Programming --
2.8.Notes --
2.9.Exercises --
3.Linear Programming Models: Asset-Liability Management --
3.1.Dedication --
3.2.Sensitivity Analysis --
3.3.Immunization --
3.4.Some Practical Details about Bonds --
3.5.Other Cash Flow Problems --
3.6.Exercises --
3.7.Case Study --
4.Linear Programming Models: Arbitrage and Asset Pricing --
4.1.Arbitrage Detection in the Foreign Exchange Market --
4.2.The Fundamental Theorem of Asset Pricing --
4.3.One-Period Binomial Pricing Model --
4.4.Static Arbitrage Bounds Note continued: 4.5.Tax Clientele Effects in Bond Portfolio Management --
4.6.Notes --
4.7.Exercises --
pt. II Single-Period Models --
5.Quadratic Programming: Theory and Algorithms --
5.1.Quadratic Programming --
5.2.Numerical Quadratic Programming Solvers --
5.3.Sensitivity Analysis --
5.4.*Duality and Optimality Conditions --
5.5.*Algorithms --
5.6.Applications to Machine Learning --
5.7.Exercises --
6.Quadratic Programming Models: Mean-Variance Optimization --
6.1.Portfolio Return --
6.2.Markowitz Mean-Variance (Basic Model) --
6.3.Analytical Solutions to Basic Mean-Variance Models --
6.4.More General Mean-Variance Models --
6.5.Portfolio Management Relative to a Benchmark --
6.6.Estimation of Inputs to Mean-Variance Models --
6.7.Performance Analysis --
6.8.Notes --
6.9.Exercises --
6.10.Case Studies --
7.Sensitivity of Mean-Variance Models to Input Estimation --
7.1.Black-Litterman Model --
7.2.Shrinkage Estimation --
7.3.Resampled Efficiency Note continued: 7.4.Robust Optimization --
7.5.Other Diversification Approaches --
7.6.Exercises --
8.Mixed Integer Programming: Theory and Algorithms --
8.1.Mixed Integer Programming --
8.2.Numerical Mixed Integer Programming Solvers --
8.3.Relaxations and Duality --
8.4.Algorithms for Solving Mixed Integer Programs --
8.5.Exercises --
9.Mixed Integer Programming Models: Portfolios with Combinatorial Constraints --
9.1.Combinatorial Auctions --
9.2.The Lockbox Problem --
9.3.Constructing an Index Fund --
9.4.Cardinality Constraints --
9.5.Minimum Position Constraints --
9.6.Risk-Parity Portfolios and Clustering --
9.7.Exercises --
9.8.Case Study --
10.Stochastic Programming: Theory and Algorithms --
10.1.Examples of Stochastic Optimization Models --
10.2.Two-Stage Stochastic Optimization --
10.3.Linear Two-Stage Stochastic Programming --
10.4.Scenario Optimization --
10.5.*The L-Shaped Method --
10.6.Exercises --
11.Stochastic Programming Models: Risk Measures Note continued: 11.1.Risk Measures --
11.2.A Key Property of CVaR --
11.3.Portfolio Optimization with CVaR --
11.4.Notes --
11.5.Exercises --
pt. III Multi-Period Models --
12.Multi-Period Models: Simple Examples --
12.1.The Kelly Criterion --
12.2.Dynamic Portfolio Optimization --
12.3.Execution Costs --
12.4.Exercises --
13.Dynamic Programming: Theory and Algorithms --
13.1.Some Examples --
13.2.Model of a Sequential System (Deterministic Case) --
13.3.Bellman's Principle of Optimality --
13.4.Linear-Quadratic Regulator --
13.5.Sequential Decision Problem with Infinite Horizon --
13.6.Linear-Quadratic Regulator with Infinite Horizon --
13.7.Model of Sequential System (Stochastic Case) --
13.8.Notes --
13.9.Exercises --
14.Dynamic Programming Models: Multi-Period Portfolio Optimization --
14.1.Utility of Terminal Wealth --
14.2.Optimal Consumption and Investment --
14.3.Dynamic Trading with Predictable Returns and Transaction Costs Note continued: 14.4.Dynamic Portfolio Optimization with Taxes --
14.5.Exercises --
15.Dynamic Programming Models: the Binomial Pricing Model --
15.1.Binomial Lattice Model --
15.2.Option Pricing --
15.3.Option Pricing in Continuous Time --
15.4.Specifying the Model Parameters --
15.5.Exercises --
16.Multi-Stage Stochastic Programming --
16.1.Multi-Stage Stochastic Programming --
16.2.Scenario Optimization --
16.3.Scenario Generation --
16.4.Exercises --
17.Stochastic Programming Models: Asset-Liability Management --
17.1.Asset-Liability Management --
17.2.The Case of an Insurance Company --
17.3.Option Pricing via Stochastic Programming --
17.4.Synthetic Options --
17.5.Exercises --
pt. IV Other Optimization Techniques --
18.Conic Programming: Theory and Algorithms --
18.1.Conic Programming --
18.2.Numerical Conic Programming Solvers --
18.3.Duality and Optimality Conditions --
18.4.Algorithms --
18.5.Notes --
18.6.Exercises --
19.Robust Optimization Note continued: 19.1.Uncertainty Sets --
19.2.Different Flavors of Robustness --
19.3.Techniques for Solving Robust Optimization Models --
19.4.Some Robust Optimization Models in Finance --
19.5.Notes --
19.6.Exercises --
20.Nonlinear Programming: Theory and Algorithms --
20.1.Nonlinear Programming --
20.2.Numerical Nonlinear Programming Solvers --
20.3.Optimality Conditions --
20.4.Algorithms --
20.5.Estimating a Volatility Surface --
20.6.Exercises --
Appendices --
Appendix Basic Mathematical Facts --
A.1.Matrices and Vectors --
A.2.Convex Sets and Convex Functions --
A.3.Calculus of Variations: the Euler Equation.
