| Description |
1 online resource (1 volume) |
| Bibliography |
Includes bibliographical references and indexes. |
| Contents |
Preface -- Measure theory -- Sets and sequences -- Measures -- Extension of measures -- Lebesgue Stieltjee measures -- Measurable functions -- Lebesgue integration -- The Radon Nikodym theorem -- LP spaces -- Convergence -- Product measures -- Probability theory -- Events and random variables -- Independence -- Expectation -- Conditional expectation -- Inequalities -- Law of large numbers -- Characteristic functions -- Discrete distributions -- Continuous distributions -- Central limit theorems -- Stochastic processes -- Martingales -- Stopping times -- Martingale inequalities -- Martingale convergence theorems -- Random walks -- Poisson processes -- Brownian motions -- Markov processes -- Levy processes -- Stochastic calculus -- The wiener integral -- The it "o" integral -- Extension of it "o" integrals -- Martingale stochastic integrals -- The it o's formula -- Martingale representation theorem -- Change of measure -- Stochastic differential equations -- Libor market models -- Diffusions -- The Feyn Mankac formula -- Stochastic financial models -- Discretetime models -- Blackscholes -- Pathdependent options -- American options -- Instantaneous forward rate models. |
| Summary |
An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of num. |
| Subject |
Finance -- Mathematical models.
|
|
Social sciences -- Research -- Statistical methods.
|
|
Finances -- Modèles mathématiques. |
|
Sciences sociales -- Recherche -- Méthodes statistiques. |
|
Finance -- Mathematical models |
|
Social sciences -- Research -- Statistical methods |
| Added Author |
Ma, Chaoqun (Professor), author.
|
|
Xie, Hong (Financial expert), author.
|
| Other Form: |
Print version: Gan, Guojun, 1979- Measure, probability, and mathematical finance. Hoboken, New Jersey : Wiley, [2014] 9781118831960 (DLC) 2013034292 (OCoLC)858126206 |
| ISBN |
1118831969 |
|
9781118831960 |
|
1118831985 |
|
9781118831984 |
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