Optimal Stopping and Applications

Thomas S. Ferguson
Mathematics Department, UCLA

• Chapter 1. Stopping Rule Problems.

  1.1 The Definition of the Problem.

  1.2 Examples.

  1.3 Exercises.

• Chapter 2. Finite Horizon Problems.

  2.1 The Classical Secretary Problem.

  2.2 Arbitrary Monotonic Utility.

  2.3 Variations.

  2.4 The Cayley-Moser Problem.

  2.5 The Parking Problem.

  2.6 Exercises.

• Chapter 3. The Existence of Optimal Rules.

  3.1 Regular Stopping Rules.

  3.2 The Principle of Optimality and the Optimality Equation.

  3.3 The Wald Equation.

  3.4 Prophet Inequalities.

  3.5 Exercises.

• Chapter 4. Applications. Markov Models.

  4.1 Selling an Asset With and Without Recall.

  4.2 Stopping a Discounted Sum.

  4.3 Stopping a Sum With Negative Drift.

  4.4 Rebounding From Failures.

  4.5 Testing Simple Statistical Hypotheses.

  4.6 Maximizing the Average.

  4.7 Exercises.

  4.A Appendix.

• Chapter 5. Monotone Stopping Rule Problems.

  5.1 The k-Stage Look-Ahead Rule.

  5.2 Monotone Stopping Rule Problems.

  5.3 Approximation of the Infinite Problem by Finite Horizon Problems.

  5.4 Examples.

  5.5 Exercises.

• Chapter 6. Maximizing the Rate of Return.

  6.1 Relation to Stopping Rule Problems.

  6.2 House Selling.

  6.3 Sum of Discounted Returns.

  6.4 Maintenance.

  6.5 An Inventory Problem.

  6.6 Exercises.

• Chapter 7. Bandit Problems.

  7.1 Introduction.

  7.2 The One-Armed Bandit.

  7.3 The Gittins Index Theorem.

• Solutions to the Exercises.

• References.

• Index.