TY  - BOOK
AU  - Gan,Guojun
TI  - Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach
T2  - New York Academy of Sciences Series
SN  - 9781118831984
AV  - HG106 .G36 2014 
U1  - 332.01/5195 
PY  - 2014///
CY  - Newark
PB  - John Wiley & Sons, Incorporated
KW  - Finance-Mathematical models
KW  - Social sciences-Research-Statistical methods
KW  - Electronic books
N1  - Intro -- Half Title page -- Title page -- Copyright page -- Dedication -- Preface -- Financial Glossary -- Part I: Measure Theory -- Chapter 1: Sets and Sequences -- 1.1 Basic Concepts and Facts -- 1.2 Problems -- 1.3 Hints -- 1.4 Solutions -- 1.5 Bibliographic Notes -- Chapter 2: Measures -- 2.1 Basic Concepts and Facts -- 2.2 Problems -- 2.3 Hints -- 2.4 Solutions -- 2.5 Bibliographic Notes -- Chapter 3: Extension of Measures -- 3.1 Basic Concepts and Facts -- 3.2 Problems -- 3.3 Hints -- 3.4 Solutions -- 3.5 Bibliographic Notes -- Chapter 4: Lebesgue-Stieltjes Measures -- 4.1 Basic Concepts and Facts -- 4.2 Problems -- 4.3 Hints -- 4.4 Solutions -- 4.5 Bibliographic Notes -- Chapter 5: Measurable Functions -- 5.1 Basic Concepts and Facts -- 5.2 Problems -- 5.3 Hints -- 5.4 Solutions -- 5.5 Bibliographic Notes -- Chapter 6: Lebesgue Integration -- 6.1 Basic Concepts and Facts -- 6.2 Problems -- 6.3 Hints -- 6.4 Solutions -- 6.5 Bibliographic Notes -- Chapter 7: The Radon-Nikodym Theorem -- 7.1 Basic Concepts and Facts -- 7.2 Problems -- 7.3 Hints -- 7.4 Solutions -- 7.5 Bibliographic Notes -- Chapter 8: LP Spaces -- 8.1 Basic Concepts and Facts -- 8.2 Problems -- 8.3 Hints -- 8.4 Solutions -- 8.5 Bibliographic Notes -- Chapter 9: Convergence -- 9.1 Basic Concepts and Facts -- 9.2 Problems -- 9.3 Hints -- 9.4 Solutions -- 9.5 Bibliographic Notes -- Chapter 10: Product Measures -- 10.1 Basic Concepts and Facts -- 10.2 Problems -- 10.3 Hints -- 10.4 Solutions -- 10.5 Bibliographic Notes -- Part II: Probability Theory -- Chapter 11: Events and Random Variables -- 11.1 Basic Concepts and Facts -- 11.2 Problems -- 11.3 Hints -- 11.4 Solutions -- 11.5 Bibliographic Notes -- Chapter 12: Independence -- 12.1 Basic Concepts and Facts -- 12.2 Problems -- 12.3 Hints -- 12.4 Solutions -- 12.5 Bibliographic Notes -- Chapter 13: Expectation; 13.1 Basic Concepts and Facts -- 13.2 Problems -- 13.3 Hints -- 13.4 Solutions -- 13.5 Bibliographic Notes -- Chapter 14: Conditional Expectation -- 14.1 Basic Concepts and Facts -- 14.2 Problems -- 14.3 Hints -- 14.4 Solutions -- 14.5 Bibliographic Notes -- Chapter 15: Inequalities -- 15.1 Basic Concepts and Facts -- 15.2 Problems -- 15.3 Hints -- 15.4 Solutions -- 15.5 Bibliographic Notes -- Chapter 16: Law of Large Numbers -- 16.1 Basic Concepts and Facts -- 16.2 Problems -- 16.3 Hints -- 16.4 Solutions -- 16.5 Bibliographic Notes -- Chapter 17: Characteristic Functions -- 17.1 Basic Concepts and Facts -- 17.2 Problems -- 17.3 Hints -- 17.4 Solutions -- 17.5 Bibliographic Notes -- Chapter 18: Discrete Distributions -- 18.1 Basic Concepts and Facts -- 18.2 Problems -- 18.3 Hints -- 18.4 Solutions -- 18.5 Bibliographic Notes -- Chapter 19: Continuous Distributions -- 19.1 Basic Concepts and Facts -- 19.2 Problems -- 19.3 Hints -- 19.4 Solutions -- 19.5 Bibliographic Notes -- Chapter 20: Central Limit Theorems -- 20.1 Basic Concepts and Facts -- 20.2 Problems -- 20.3 Hints -- 20.4 Solutions -- 20.5 Bibliographic Notes -- Part III: Stochastic Processes -- Chapter 21: Stochastic Processes -- 21.1 Basic Concepts and Facts -- 21.2 Problems -- 21.3 Hints -- 21.4 Solutions -- 21.5 Bibliographic Notes -- Chapter 22: Martingales -- 22.1 Basic Concepts and Facts -- 22.2 Problems -- 22.3 Hints -- 22.4 Solutions -- 22.5 Bibliographic Notes -- Chapter 23: Stopping Times -- 23.1 Basic Concepts and Facts -- 23.2 Problems -- 23.3 Hints -- 23.4 Solutions -- 23.5 Bibliographic Notes -- Chapter 24: Martingale Inequalities -- 24.1 Basic Concepts and Facts -- 24.2 Problems -- 24.3 Hints -- 24.4 Solutions -- 24.5 Bibliographic Notes -- Chapter 25: Martingale Convergence Theorems -- 25.1 Basic Concepts and Facts -- 25.2 Problems -- 25.3 Hints -- 25.4 Solutions; 25.5 Bibliographic Notes -- Chapter 26: Random Walks -- 26.1 Basic Concepts and Facts -- 26.2 Problems -- 26.3 Hints -- 26.4 Solutions -- 26.5 Bibliographic Notes -- Chapter 27: Poisson Processes -- 27.1 Basic Concepts and Facts -- 27.2 Problems -- 27.3 Hints -- 27.4 Solutions -- 27.5 Bibliographic Notes -- Chapter 28: Brownian Motion -- 28.1 Basic Concepts and Facts -- 28.2 Problems -- 28.3 Hints -- 28.4 Solutions -- 28.5 Bibliographic Notes -- Chapter 29: Markov Processes -- 29.1 Basic Concepts and Facts -- 29.2 Problems -- 29.3 Hints -- 29.4 Solutions -- 29.5 Bibliographic Notes -- Chapter 30: Lévy Processes -- 30.1 Basic Concepts and Facts -- 30.2 Problems -- 30.3 Hints -- 30.4 Solutions -- 30.5 Bibliographic Notes -- Part IV: Stochastic Calculus -- Chapter 31: The Wiener Integral -- 31.1 Basic Concepts and Facts -- 31.2 Problems -- 31.3 Hints -- 31.4 Solutions -- 31.5 Bibliographic Notes -- Chapter 32: The Itô Integral -- 32.1 Basic Concepts and Facts -- 32.2 Problems -- 32.3 Hints -- 32.4 Solutions -- 32.5 Bibliographic Notes -- Chapter 33: Extension of the Itô Integral -- 33.1 Basic Concepts and Facts -- 33.2 Problems -- 33.3 Hints -- 33.4 Solutions -- 33.5 Bibliographic Notes -- Chapter 34: Martingale Stochastic Integrals -- 34.1 Basic Concepts and Facts -- 34.2 Problems -- 34.3 Hints -- 34.4 Solutions -- 34.5 Bibliographic Notes -- Chapter 35: The Itô Formula -- 35.1 Basic Concepts and Facts -- 35.2 Problems -- 35.3 Hints -- 35.4 Solutions -- 35.5 Bibliographic Notes -- Chapter 36: Martingale Representation Theorem -- 36.1 Basic Concepts and Facts -- 36.2 Problems -- 36.3 Hints -- 36.4 Solutions -- 36.5 Bibliographic Notes -- Chapter 37: Change of Measure -- 37.1 Basic Concepts and Facts -- 37.2 Problems -- 37.3 Hints -- 37.4 Solutions -- 37.5 Bibliographic Notes -- Chapter 38: Stochastic Differential Equations; 38.1 Basic Concepts and Facts -- 38.2 Problems -- 38.3 Hints -- 38.4 Solutions -- 38.5 Bibliographic Notes -- Chapter 39: Diffusion -- 39.1 Basic Concepts and Facts -- 39.2 Problems -- 39.3 Hints -- 39.4 Solutions -- 39.5 Bibliographic Notes -- Chapter 40: The Feynman-Kac Formula -- 40.1 Basic Concepts and Facts -- 40.2 Problems -- 40.3 Hints -- 40.4 Solutions -- 40.5 Bibliographic Notes -- Part V: Stochastic Financial Models -- Chapter 41: Discrete-Time Models -- 41.1 Basic Concepts and Facts -- 41.2 Problems -- 41.3 Hints -- 41.4 Solutions -- 41.5 Bibliographic Notes -- Chapter 42: Black-Scholes Option Pricing Models -- 42.1 Basic Concepts and Facts -- 42.2 Problems -- 42.3 Hints -- 42.4 Solutions -- 42.5 Bibliographic Notes -- Chapter 43: Path-Dependent Options -- 43.1 Basic Concepts and Facts -- 43.2 Problems -- 43.3 Hints -- 43.4 Solutions -- 43.5 Bibliographic Notes -- Chapter 44: American Options -- 44.1 Basic Concepts and Facts -- 44.2 Problems -- 44.3 Hints -- 44.4 Solutions -- 44.5 Bibliographic Notes -- Chapter 45: Short Rate Models -- 45.1 Basic Concepts and Facts -- 45.2 Problems -- 45.3 Hints -- 45.4 Solutions -- 45.5 Bibliographic Notes -- Chapter 46: Instantaneous Forward Rate Models -- 46.1 Basic Concepts and Facts -- 46.2 Problems -- 46.3 Hints -- 46.4 Solutions -- 46.5 Bibliographic Notes -- Chapter 47: Libor Market Models -- 47.1 Basic Concepts and Facts -- 47.2 Problems -- 47.3 Hints -- 47.4 Solutions -- 47.5 Bibliographic Notes -- References -- List of Symbols -- Subject Index
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