Metamodeling for Variable Annuities (Chapman and Hall/CRC Financial Mathematics Series)

Description

This book is devoted to the mathematical methods of metamodeling that can be used to speed up the valuation of large portfolios of variable annuities. It is suitable for advanced undergraduate students, graduate students, and practitioners. It is the goal of this book to describe the computational problems and present the metamodeling approaches in a way that can be accessible to advanced undergraduate students and practitioners. To that end, the book will not only describe the theory of these mathematical approaches, but also present the implementations. Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface I: Preliminaries 1: Computational Problems in Variable Annuities 1.1 Variable Annuities 1.2 Computational Problems Related to Daily Hedging 1.3 Computational Problems Related to Financial Reporting 1.4 Summary 2: Existing Approaches 2.1 Scenario Reduction 2.1.1 Scenario Ranking 2.1.2 Representative Scenarios 2.1.3 Importance Sampling 2.1.4 Curve Fitting 2.1.5 Random Sampling 2.2 Inforce Compression 2.2.1 Cluster Modeling 2.2.2 Replicating Liabilities 2.2.3 Replicated Stratified Sampling 2.3 Summary 3: Metamodeling Approaches 3.1 A General Framework 3.2 Literature Review 3.3 Summary II: Experimental Design Methods 4: Latin Hypercube Sampling 4.1 Description of the Method 4.2 Implementation 4.3 Examples 4.4 Summary 5: Conditional Latin Hypercube Sampling 5.1 Description of the Method 5.2 Implementation 5.3 Examples 5.4 Summary 6: Hierarchical k-Means 6.1 Description of the Method 6.2 Implementation 6.3 Examples 6.4 Summary III: Metamodels 7: Ordinary Kriging 7.1 Description of the Model 7.2 Implementation 7.3 Applications 7.3.1 Ordinary Kriging with Latin Hypercube Sampling 7.3.2 Ordinary Kriging with Conditional Latin Hypercube Sampling 7.3.3 Ordinary Kriging with Hierarchical k-Means 7.4 Summary 8: Universal Kriging 8.1 Description of the Model 8.2 Implementation 8.3 Applications 8.3.1 Universal Kriging with Latin Hypercube Sampling 8.3.2 Universal Kriging with Conditional Latin Hypercube Sampling 8.3.3 Universal Kriging with Hierarchical k-Means 8.4 Summary 9: GB2 Regression Model 9.1 Description of the Model 9.2 Implementation 9.3 Applications 9.3.1 GB2 with Latin Hypercube Sampling 9.3.2 GB2 with Conditional Latin Hypercube Sampling 9.3.3 GB2 with Hierarchical k-Means 9.4 Summary 10: Rank Order Kriging 10.1 Description of the Model 10.2 Implementation 10.3 Applications 10.3.1 Rank Order Kriging with Latin Hypercube Sampling 10.3.2 Rank Order Kriging with Conditional Latin Hypercube Sampling 10.3.3 Rank Order Kriging with Hierarchical k-Means 10.4 Summary 11: Linear Model with Interactions 11.1 Description of the Model 11.2 Implementation 11.3 Applications 11.3.1 Linear Model with Latin Hypercube Sampling 11.3.2 Linear Model with Conditional Latin Hypercube Sampling 11.3.3 Linear Model with Hierarchical k-Means 11.4 Summary 12: Tree-Based Models 12.1 Description of the Model 12.2 Implementation 12.3 Applications 12.3.1 Regression Trees with Latin Hypercube Sampling 12.3.2 Regression Trees with Conditional Latin Hypercube Sampling 12.3.3 Regression Trees with Hierarchical k-Means 12.4 Summary A: Synthetic Datasets A.1 The Synthetic Inforce A.2 The Greeks Bibliography Index