Optimization, Control, and Applications of Stochastic Systems

Compiled in honor of Onésimo Hernández-Lerma, this volume offers a broad presentation of the main concepts, techniques, and methodologies in the fields of optimization and control of stochastic systems. At the same time, the book provides an overview of their wide-ranging applications and theoretical developments. These topics include various aspects of dynamic programming, discounted and average optimality criteria for discrete- and continuous-time control processes, approximation algorithms, optimal stopping, and games.

The work comprises 18 carefully selected papers written by experts in their respective fields, and explores five major themes:

• discrete-time Markov control processes; several optimality criteria; applications in inventory systems and finance; stochastic optimal control problems for diffusion; optimization.

This book will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and its applications.

Zusammenfassung

This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields.

Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.

Inhalt
1 On the Policy Iteration Algorithm for Non-degenerate Controlled Diffusions under the Ergodic Criterion.- 2 Discrete-Time Inventory Problems with Lead Time and Order-Time Constraint.- 3 Sample-Path Optimality in Average Markov Decision Chains.- 4 Approximation of Infinite Horizon Discounted Cost Markov.- 5 Reduction of Discounted Continuous-Time MDPs with Unbounded.- 6 Continuous-Time Controlled Jump Markov Processes on the Finite.- 7 Existence and Uniqueness of Solutions of SPDEs in Infinite Dimensions.- 8 A Constrained Optimization Problem with Applications to Constrained.- 9 Optimal Execution of Derivatives, a Taylor Expansion Approach.- 10 A Survey of Some Model-Based Methods for Global Optimization.- 11 Constrained Optimality for First Passage Criteria in Semi-Markov.- 12 Infinite-Horizon Optimal Control Problems for Hybrid Switching.- 13 Fluid Approximations to Markov Decision Processes with Local.- 14 Minimizing Ruin Probabilities by Reinsurance and Investment: a Markovian Decision Approach.- 15 Estimation of the Optimality Deviation in Discounted Semi-Markov.- 16 Discrete Time Approximations of Continuous Time Finite Horizon.- 17 A Direct Approach to the Solution of Optimal Multiple-Stopping.- 18 On the Regularity Property of Semi-Markov Processes with Borel State Spaces.