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This book offers a comprehensive introduction to Markov decision process and reinforcement learning fundamentals using common mathematical notation and language. Its goal is to provide a solid foundation that enables readers to engage meaningfully with these rapidly evolving fields. Topics covered include finite and infinite horizon models, partially observable models, value function approximation, simulation-based methods, Monte Carlo methods, and Q-learning. Rigorous mathematical concepts and algorithmic developments are supported by numerous worked examples. As an up-to-date successor to Martin L. Puterman's influential 1994 textbook, this volume assumes familiarity with probability, mathematical notation, and proof techniques. It is ideally suited for students, researchers, and professionals in operations research, computer science, engineering, and economics.
Providing comprehensive yet accessible coverage, this is the first graduate-level textbook dedicated to the mathematical theory of risk measures. It explains how economic and financial principles result in a profound mathematical theory that allows us to quantify risk in monetary terms, giving rise to risk measures. Each chapter is designed to match the length of one or two lectures, covering the core theory in a self-contained manner, with exercises included in every chapter. Additional material sections then provide further background and insights for those looking to delve deeper. This two-layer modular design makes the book suitable as the basis for diverse lecture courses of varying length and level, and a valuable resource for researchers.
Dynamic stochastic general equilibrium (DSGE) models have begun to dominate the field of macroeconomic theory and policy-making. These models describe the evolution of macroeconomic activity as a recursive sequence of outcomes based upon the optimal decision rules of rational households, firms and policy-makers. Whilst posing a micro-founded dynamic optimisation problem for agents under uncertainty, such models have been shown to be both analytically tractable and sufficiently rich for meaningful policy analysis in a wide class of macroeconomic problems, for example, monetary and fiscal policy, economic cycles and growth and capital flows. This volume collects specially commissioned papers from leading researchers, which pull together some of the key results in diverse areas. This book will promote research using optimising models and inform researchers, post-graduate students and economists in policy-oriented organisations of some of the key findings and policy implications.