Measure, probability, and mathematical finance a problem-oriented approach
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 im...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Hoboken, New Jersey
Wiley
2014
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| Subjects: | |
| Online Access: | |
| Collection: | O'Reilly - Collection details see MPG.ReNa |
Table of 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
- Includes bibliographical references and indexes