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Stochastic Modeling and Optimization : With Applications in Queues, Finance, and Supply Chains

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概要 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.続きを見る
目次 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 between Artificial 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 The Minimum 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.
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登録日 2020.06.27
更新日 2020.06.28