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Preface Common Symbols Common Abbreviations Introduction Bellman Equations Finite-Horizon Job Search Infinite Horizon Stability and Contractions Vector Space Nonlinear Systems Successive Approximation Finite-Dimensional Function Space Infinite-Horizon Job Search Values and Policies Computation Chapter Notes Operators and Fixed Points Stability Conjugate Maps Local Stability Convergence Rates Gradient-Based Methods Order Partial Orders The Case of Pointwise Order Order-Preserving Maps Stochastic Dominance Parametric Monotonicity Matrices and Operators Nonnegative Matrices A Lake Model Linear Operators Chapter Notes Markov Dynamics Foundations Markov Chains Stationarity and Ergodicity Approximation Conditional Expectations Mathematical Expectations Geometric Sums Job Search Revisited Job Search with Markov State Job Search with Separation Chapter Notes Optimal Stopping Introduction to Optimal Stopping Theory Firm Valuation with Exit Monotonicity Continuation Values Further Applications American Options Research and Development Chapter Notes Markov Decision Processes Definition and Properties The MDP Model Examples Optimality Algorithms Applications Optimal Inventories Optimal Savings with Labor Income Optimal Investment Modified Bellman Equations Structural Estimation The Gumbel Max Trick Optimal Savings with Stochastic Returns on Wealth Q-Factors Operator Factorizations Chapter Notes Stochastic Discounting Time-Varying Discount Factors Valuation Testing the Spectral Radius Condition Fixed Point Results Optimality with State-Dependent Discounting MDPs with State-Dependent Discounting Inventory Management Revisited Asset Pricing Introduction to Asset Pricing Nonstationary Dividends Incomplete Markets Chapter Notes Nonlinear Valuation Beyond Contraction Maps Knaster–Tarski for Function Space Concavity, Convexity and Stability A Power-Transformed Affine Equation Recursive Preferences Motivation: Optimal Savings Risk-Sensitive Preferences Epstein–Zin Preferences General Representations Koopmaps Operators A Blackwell-Type Condition Uzawa Aggregation Chapter Notes Recursive Decision Processes Definition and Properties Defining RDPs Lifetime Value Optimality Topologically Conjugate RDPs Types of RDPs Contracting RDPs Eventually Contracting RDPs Convex and Concave RDPs Further Applications Risk-Sensitive RDPs Adversarial Agents Ambiguity and Robustness Smooth Ambiguity Minimization Chapter Notes Abstract Dynamic Programming Abstract Dynamic Programs Preliminaries Abstract Dynamic Programs Optimality Optimality Results for RDPs Min-Optimality Isomorphic Dynamic Programs Isomorphic ADPs Anti-Isomorphic ADPs Application: Epstein–Zin Without Irreducibility Subordinate ADPs Definition and Properties Optimality Application Chapter Notes Continuous Time Continuous Time Markov Chains Background Continuous Time Flows Markov Semigroups Continuous Time Markov Chains Continuous Time Markov Decision Processes Valuation Constructing a Decision Process Optimality Application: Job Search Chapter Notes I Appendices Suprema and Infima Sets and Functions Some Properties of the Real Line Max and Min Remaining Proofs Chapter 3 Results Chapter 6 Results Chapter 7 Results Chapter 9 Results Solutions to Selected Exercises