Algorithms for Worst-Case Design and Applications to Risk Management

By Berç Rustem; Melendres Howe | Go to book overview

Contents
Prefacexiii
Chapter 1. Introduction to minimax1
   1 Background and Notation1
1.1 Linear Independence5
1.2 Tangent Cone, Normal Cone and Epigraph7
1.3 Subgradiemts and Subdifferentials of Convex Functions7
   2 Continuous Minimax10
   3 Optimality Conditions and Robustness of Minimax11
3.1 The Haar Condition 13
   4 Saddle Points and Saddle Point Conditions15
References17
Comments and Notes18
Chapter 2. A survey of continuous minimax algorithms23
   1 Introduction23
   2 The Algorithm of Chaney25
   3 The Algorithm of Panin30
   4 The Algorithm of Kiwiel31
References33
Comments and Notes34
Chapter 3. Algorithms for computing saddle points37
   1 Computation of Saddle Points37
1.1 Saddle Point Equilibria37
1.2 Solution of Systems of Equations40
   2 The Algorithms42
2.1 A Gradient-based Algorithm for Unconstrained Saddle Points42
2.2 Quadratic Approximation Algorithm for Constrained Minimax Saddle Points44
2.3 Interior Point Saddle Point Algorithm for Constrained Problems45
2.4 Quasi-Newton Algorithm for Nonlinear Systems49
   3 Global Convergence of Newton-type Algorithms50
   4 Achievement of Unit Stepsizes and Superlinear Convergence54
   5 Concluding Remarks58
References58
Comments and Notes59

-vii-

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Algorithms for Worst-Case Design and Applications to Risk Management
Table of contents

Table of contents

  • Title Page *
  • Algorithms for Worst-Case Design and Applications to Risk Management *
  • Contents vii
  • Preface xiii
  • Chapter 1 - Introduction to Minimax 1
  • References 17
  • Comments and Notes *
  • Chapter 2 - A Survey of Continuous Minimax Algorithms 23
  • References *
  • Comments and Notes *
  • Chapter 3 - Algorithms for Computing Saddle Points 37
  • References *
  • Comments and Notes *
  • Chapter 4 - A Quasi-Newton Algorithm for Continuous Minimax 63
  • References *
  • Appendix A - Implementation Issues *
  • Appendix B - Motivation for the Search Direction D̄ *
  • Comments and Notes *
  • Chapter 5 - Numerical Experiments with Continuous Minimax Algorithms 93
  • References 119
  • Chapter 6 - Minimax as a Robust Strategy for Discrete Rival Scenarios 121
  • References *
  • Chapter 7 - Discrete Minimax Algorithm for Equality and Inequality Constrained Models 139
  • References *
  • Chapter 8 - A Continuous Minimax Strategy for Options Hedging 179
  • References *
  • Appendix A - Weighting Hedge Recommendations, Variant B* *
  • Appendix B - Numerical Examples 237
  • Comments and Notes 244
  • Chapter 9 - Minimax and Asset Allocation Problems 247
  • References *
  • Comments and Notes *
  • Chapter 10 - Asset/liability Management under Uncertainty 291
  • References *
  • Comments and Notes *
  • Chapter 11 - Robust Currency Management 341
  • References *
  • Appendix - Currency Forecasting *
  • Comments and Notes *
  • Index 381
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