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| Preface | |
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| Introduction | |
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| Notes | |
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| Mathematical Preliminaries | |
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| Stochastic Processes, Brownian Motions, and Diffusions | |
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| Random Variables and Stochastic Processes | |
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| Independence | |
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| Wiener Processes and Brownian Motions | |
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| Random Walk Approximation of a Brownian Motion | |
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| Stopping Times | |
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| Strong Markov Property | |
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| Diffusions | |
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| Discrete Approximation of an Ornstein-Uhlenbeck Process | |
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| Notes | |
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| Stochastic Integrals and Ito's Lemma | |
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| The Hamilton-Jacobi-Bellman Equation | |
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| Stochastic Integrals | |
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| Ito's Lemma | |
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| Geometric Brownian Motion | |
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| Occupancy Measure and Local Time | |
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| Tanaka's Formula | |
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| The Kolmogorov Backward Equation | |
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| The Kolmogorov Forward Equation | |
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| Notes | |
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| Martingales | |
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| Definition and Examples | |
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| Martingales Based on Eigenvalues | |
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| The Wald Martingale | |
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| Sub- and Supermartingales | |
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| Optional Stopping Theorem | |
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| Optional Stopping Theorem, Extended | |
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| Martingale Convergence Theorem | |
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| Notes | |
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| Useful Formulas for Brownian Motions | |
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| Stopping Times Defined by Thresholds | |
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| Expected Values for Wald Martingales | |
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| The Functions [psi] and [Psi] | |
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| ODEs for Brownian Motions | |
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| Solutions for Brownian Motions When r = 0 | |
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| Solutions for Brownian Motions When r > 0 | |
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| ODEs for Diffusions | |
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| Solutions for Diffusions When r = 0 | |
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| Solutions for Diffusions When r > 0 | |
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| Notes | |
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| Impulse Control Models | |
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| Exercising an Option | |
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| The Deterministic Problem | |
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| The Stochastic Problem: A Direct Approach | |
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| Using the Hamilton-Jacobi-Bellman Equation | |
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| An Example | |
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| Notes | |
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| Models with Fixed Costs | |
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| A Menu Cost Model | |
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| Preliminary Results | |
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| Optimizing: A Direct Approach | |
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| Using the Hamilton-Jacobi-Bellman Equation | |
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| Random Opportunities for Costless Adjustment | |
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| An Example | |
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| Notes | |
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| Models with Fixed and Variable Costs | |
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| An Inventory Model | |
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| Preliminary Results | |
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| Optimizing: A Direct Approach | |
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| Using the Hamilton-Jacobi-Bellman Equation | |
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| Long-Run Averages | |
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| Examples | |
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| Strictly Convex Adjustment Costs | |
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| Notes | |
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| Models with Continuous Control Variables | |
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| Housing and Portfolio Choice with No Transaction Cost | |
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| The Model with Transaction Costs | |
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| Using the Hamilton-Jacobi-Bellman Equation | |
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| Extensions | |
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| Notes | |
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| Instantaneous Control Models | |
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| Regulated Brownian Motion | |
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| One- and Two-Sided Regulators | |
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| Discounted Values | |
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| The Stationary Distribution | |
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| An Inventory Example | |
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| Notes | |
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| Investment: Linear and Convex Adjustment Costs | |
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| Investment with Linear Costs | |
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| Investment with Convex Adjustment Costs | |
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| Some Special Cases | |
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| Irreversible Investment | |
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| Irreversible Investment with Two Shocks | |
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| A Two-Sector Economy | |
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| Notes | |
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| Aggregation | |
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| An Aggregate Model with Fixed Costs | |
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| The Economic Environment | |
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| An Economy with Monetary Neutrality | |
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| An Economy with a Phillips Curve | |
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| Optimizing Behavior and the Phillips Curve | |
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| Motivating the Loss Function | |
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| Notes | |
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| Continuous Stochastic Processes | |
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| Modes of Convergence | |
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| Continuous Stochastic Processes | |
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| Wiener Measure | |
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| Nondifferentiability of Sample Paths | |
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| Notes | |
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| Optional Stopping Theorem | |
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| Stopping with a Uniform Bound, T < N | |
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| Stopping with Pr { T < [infinity]} = 1 | |
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| Notes | |
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| References | |
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| Index | |