Conditional Monte Carlo - Fu, Michael C.

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Résumé :
Conditional Monte Carlo: Gradient Estimation and Optimization Applications deals with various gradient estimation techniques of perturbation analysis based on the use of conditional expectation. The primary setting is discrete-event stochastic simulation. This book presents applications to queueing and inventory, and to other diverse areas such as financial derivatives, pricing and statistical quality control. To researchers already in the area, this book offers a unified perspective and adequately summarizes the state of the art. To researchers new to the area, this book offers a more systematic and accessible means of understanding the techniques without having to scour through the immense literature and learn a new set of notation with each paper. To practitioners, this book provides a number of diverse application areas that makes the intuition accessible without having to fully commit to understanding all the theoretical niceties. In sum, the objectives of this monograph are two-fold: to bring together many of the interesting developments in perturbation analysis based on conditioning under a more unified framework, and to illustrate the diversity of applications to which these techniques can be applied. Conditional Monte Carlo: Gradient Estimation and Optimization Applications is suitable as a secondary text for graduate level courses on stochastic simulations, and as a reference for researchers and practitioners in industry.

Sommaire:
1 Introduction.- 1.1 Derivatives of Random Variables.- 1.2 Infinitesimal Perturbation Analysis.- 1.3 The Role of Representations.- 1.4 Basic Theoretical Tools.- 1.5 Derivatives of Measures.- 1.6 A Simple Illustrative Example.- 1.7 Two Views of Conditioning.- 1.8 A Brief Perturbation Analysis Lexicon.- 1.9 Summary.- 2 Three Extended Examples.- 2.1 Renewal Process.- 2.2 Single-Server Queue.- 2.3 (s, S) Inventory System.- 2.4 Summary.- 3 Conditional Monte Carlo Gradient Estimation.- 3.1 The GSMP Framework.- 3.2 Infinitesimal Perturbation Analysis.- 3.3 Gradient Estimation via Conditioning.- 3.4 Discontinuous Performance Measures.- 3.5 Other Stopping Times.- 3.6 Long-Run Average Performance Measures.- 3.7 Higher Order Derivative Estimators.- 4 Links to Other Settings.- 4.1 Special Cases.- 4.2 An Alternative Characterization.- 4.3 Likelihood Ratio Method.- 4.4 Rare Perturbation Analysis.- 4.5 Weak Derivatives.- 4.6 Discontinuous Perturbation Analysis.- 4.7 Augmented Infinitesimal Perturbation Analysis.- 4.8 Likelihood Ratio Method via Conditioning.- 5 Synopsis and Preview.- 5.1 Summary of Main Results.- 5.2 Efficient Implementation.- 5.3 Gradient-Based Optimization.- 5.4 Preview of Applications.- 6 Queueing Systems.- 6.1 Single Queue Notation.- 6.2 Timing Parameters.- 6.3 Discontinuous Performance Measures.- 6.4 Finite Capacity Queue.- 6.5 Priority Queue.- 6.6 Multiple Servers Second Derivative.- 6.7 Multiple Non-Identical Servers.- 6.8 The Routing Problem.- 6.9 Other Threshold-Based Parameters.- 6.10 An Optimization Example.- 6.11 Multi-Class Queueing Network.- 7 (s, S) Inventory Systems.- 7.1 Standard Periodic Review Model.- 7.2 Service Level Performance Measures.- 7.3 Hybrid Periodic Review Model.- 8 Other Applications.- 8.1 A Component Replacement Problem.- 8.2 Pricing of Financial Derivatives.- 8.3 Design of Control Charts.- References.