How to Gamble If You Must: Inequalities for Stochastic Processes (Dover Books on Mathematics)

Cover -- Title Page -- Copyright Page -- Dedication -- Contents -- 1. The Problem -- 2. Preview -- 3. Antecedents -- 1. Introduction -- 1. Introduction -- 2. Fortunes And Histories -- 3. Gambles -- 4. Gambling House -- 5. Strategies -- 6. The Integral Generated By a Strategy -- 7. Finitary Mappings -- 8. Inductively Integrable Functions -- 9. Stop Rules, Policies, and Terminal Fortunes -- 10. The Utility of Fortunes, Policies, and Houses -- 11. Incomplete Stop Rules -- 12. Functions That Majorize U -- 13. Digression About Countable Additivity -- 14. U Is Excessive For T -- 15. Limited Playing Time -- 16. Continuous Gambling Houses -- 2. Formulation of The Abstract Gambler'S Problem -- 1. Introduction -- 2. The Utility of A Strategy -- 3. Strategic Utility -- 4. Stagnant Strategies -- 5. Optimal Strategies -- 6. Thrifty Strategies -- 7. Equalizing Strategies -- 8. Optimal Strategies Again -- 9. Stationary Families -- 3. Strategies -- 1. Introduction -- 2. THE CASINO INEQUALITY -- 3. Exploration of The Casino Inequality -- 4. The Three Special Types of Casinos -- 5. How Nice Casinos Are -- 6. The Casino-Function Semigroup -- 7. Rich Man'S, Poor Man'S, snd Inclusive Casinos -- 8. The Special Casino Inequalities Do Not Imply The General One -- 4. Casinos With Fixed Goals -- 1. Introduction -- 2. The Utility of Bold Strategies -- 3. For w