How to Gamble If You Must: Inequalities for Stochastic Processes

Description

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 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 &lt 1/2, Bold Play Is Optimal -- 4. Other Optimal Strategies For w &lt 1/2 -- 5. Limited Playing Time -- 6. The Taxed Coin -- 5. Red-And-Black -- 1. Introduction -- 2. The Utility of Bold Strategies -- 3. Bold Play Is Optimal For Subfair Primitive Casinos -- 4. Digression About N -- 5. Other Optimal Strategies For W &lt T -- 6. Limited Playing Time -- 7. Primitive Casinos In Relation To General Casinos -- 8. More About Primitive Casinos Functions -- 9. Uniform Roulette -- 6. Primitive Casinos -- 1. Introduction. 2. Composition -- 3. Permitted Sets of Gambles -- 4. Full Houses -- 5. Permitted Houses -- 7. Some General Principles -- 1. Introduction -- 2. Domination -- 3. Monotone Houses -- 4. Increasing Full Houses -- 5. Full-House Casinoes -- 6. Stationary Full Houses -- 7. Exponential Houses -- 8. Houses on The Real Line -- 1. Introduction -- 2. Income-Tax Casinos -- 3. The Casino That Takes A Cut Of The Stake -- 4. Houses of Inequity -- 9. Three Particular Kinds of Casinos -- 1. Introduction -- 2. Limited Playing Time -- 3. Conventional Lotteries -- 4. General Lotteries -- 5. Proportional Strategies -- 10. One-Lottery Strategies -- 1. Introduction -- 2. Fair Lotteries Can Generate Subfair Casinos -- 3. When Is A Casino Fair? -- 4. Fair, Simple-Lottery Casinos -- 5. Fair, One-Game Casinos -- 6. Optimal Strategies For Fair Casinos -- 11. Fair Casinos -- 1. Introduction -- 2. Fortunes -- 3. Opinion As A Component of Fortune -- 4. Nonleavable Houses -- 5. Discounting The Future -- 6. A Different Approach To The Indefinite Future -- 7. Dynamic Programming -- 8. Bayesian Statistics -- 9. Stochastic Processes -- 12. THe Scope of Gambler'S Problems -- Bibliography -- Bibliographic Supplement (1975) -- Bibliographic Supplement (2014) -- Index of Persons -- Subject Index -- Index of Symbols -- Index of Open Problems -- Remarks on Open Problems -- Appendix on Finite Additivity.