Stochastic Modeling and Optimization : With Applications in Queues, Finance, and Supply Chains (Springer Series in Operations Research) （2003. 480 p.）

Ed. by D. D. Yao, H. Zhang and X. Y. Zhou

SPRINGER, BERLIN（2003発売）

• 製本 Hardcover:ハードカバー版／ページ数 480 p.
• 商品コード 9780387955827

Full Description

The objective of this volume is to highlight through a collection of chap­ ters some of the recent research works in applied prob ability, specifically stochastic modeling and optimization. The volume is organized loosely into four parts. The first part is a col­ lection of several basic methodologies: singularly perturbed Markov chains (Chapter 1), and related applications in stochastic optimal control (Chapter 2); stochastic approximation, emphasizing convergence properties (Chapter 3); a performance-potential based approach to Markov decision program­ ming (Chapter 4); and interior-point techniques (homogeneous self-dual embedding and central path following) applied to stochastic programming (Chapter 5). The three chapters in the second part are concerned with queueing the­ ory. Chapters 6 and 7 both study processing networks - a general dass of queueing networks - focusing, respectively, on limit theorems in the form of strong approximation, and the issue of stability via connections to re­ lated fluid models. The subject of Chapter 8 is performance asymptotics via large deviations theory, when the input process to a queueing system exhibits long-range dependence, modeled as fractional Brownian motion.

Contents

1 Discrete-time Singularly Perturbed Markov Chains.- 1.1 Singularly Perturbed Markov Chains.- 1.2 Asymptotic Expansions.- 1.3 Occupation Measures.- 1.4 Nonstationary Markov Chains and Applications.- 1.5 Notes and Remarks.- 1.6 References.- 2 Nearly Optimal Controls of Markovian Systems.- 2.1 Singularly Perturbed MDP.- 2.2 Hybrid LQG Control.- 2.3 Conclusions.- 2.4 References.- 3 Stochastic Approximation, with Applications.- 3.1 SA Algorithms.- 3.2 General Convergence Theorems by TS Method.- 3.3 Convergence Theorems Under State-Independent Conditions.- 3.4 Applications.- 3.5 Notes.- 3.6 References.- 4 Performance Potential Based Optimization and MDPs.- 4.1 Sensitivity Analysis and Performance Potentials.- 4.2 Markov Decision Processes.- 4.3 Problems with Discounted Performance Criteria.- 4.4 Single Sample Path Based Implementations.- 4.5 Time Aggregation.- 4.6 Connections to Perturbation Analysis.- 4.7 Application Examples.- 4.8 Notes.- 4.9 References.- 5 An Interior-Point Approach to Multi-Stage Stochastic Programming.- 5.1 Two-Stage Stochastic Linear Programming.- 5.2 A Case Study.- 5.3 Multiple Stage Stochastic Programming.- 5.4 An Interior Point Method.- 5.5 Finding Search Directions.- 5.6 Model Diagnosis.- 5.7 Notes.- 5.8 References.- 6 A Brownian Model of Stochastic Processing Networks.- 6.1 Preliminaries.- 6.2 Stochastic Processing Network Model.- 6.3 Examples of Stochastic Processing Networks.- 6.4 Brownian Model for Stochastic Processing Network.- 6.5 Brownian Approximation via Strong Approximation.- 6.6 Notes.- 6.7 Appendix: Strong Approximation vs. Heavy Traffic Approximation.- 6.8 References.- 7 Stability of General Processing Networks.- 7.1 Motivating Simulations.- 7.2 Open Processing Networks.- 7.3 Network and Fluid Model Equations.- 7.4 Connection betweenArtificial and Standard Fluid Models.- 7.5 Examples of Stable Policies.- 7.6 Extensions.- 7.7 Appendix.- 7.8 Notes.- 7.9 References.- 8 Large Deviations, Long-Range Dependence, and Queues.- 8.1 Fractional Brownian Motion and a Related Filter.- 8.2 Moderate Deviations for Sample-Path Processes.- 8.3 MDP for the Filtered Process.- 8.4 Queueing Applications: The Workload Process.- 8.5 Verifying the Key Assumptions.- 8.6 Notes.- 8.7 References.- 9 Markowitz's World in Continuous Time, and Beyond.- 9.1 The Mean-Variance Portfolio Selection Model.- 9.2 A Stochastic LQ Control Approach.- 9.3 Efficient Frontier: Deterministic Market Parameters.- 9.4 Efficient Frontier: Random Adaptive Market Parameters.- 9.5 Efficient Frontier: Markov-Modulated Market Parameters.- 9.6 Efficient Frontier: No Short Selling.- 9.7 Mean-Variance Hedging.- 9.8 Notes.- 9.9 References.- 10 Variance Minimization in Stochastic Systems.- 10.1 Variance Minimization Problem.- 10.2 General Variance Minimization Problem.- 10.3 Variance Minimization in Dynamic Portfolio Selection.- 10.4 Variance Minimization in Dual Control.- 10.5 Notes.- 10.6 References.- 11 A Markov Chain Method for Pricing Contingent Claims.- 11.1 The Markov Chain Pricing Method.- 11.2 The Black-Scholes (1973) Pricing Model.- 11.3 The GARCH Pricing Model.- 11.4 Valuing Exotic Options.- 11.5 Appendix: The Conditional Expected Value of hT* and hT*2.- 11.6 References.- 12 Stochastic Network Models and Optimization of a Hospital System.- 12.1 A Multi-Site Service Network Model.- 12.2 Patient Flow Management.- 12.3 Capacity Design.- 12.4 Switching Costs and Quality of Service.- 12.5 Insights and Future Research Directions.- 12.6 Notes.- 12.7 References.- 13 Optimal Airline Booking Control with Cancellations.- 13.1 Preliminaries.- 13.2 TheMinimum Acceptable Fare and Threshold Control.- 13.3 Extensions of the Basic Model.- 13.4 Numerical Experiments.- 13.5 Notes.- 13.6 References.- 14 Information Revision and Decision Making in Supply Chain Management.- 14.1 Industrial Examples.- 14.2 A Multi-Period, Two-Decision Model.- 14.3 A One-Period, Multi-Information Revision Model.- 14.4 Applications.- 14.5 Notes.- 14.6 References.- About the Contributors.