Stochastic Calculus and Financial Applications | J. Michael Steele | Taschenbuch | Stochastic Modelling and Applied Probability | Paperback | X | Englisch | 2010 | Springer US | EAN 9781441928627 - Paperback

EAN (ISBN-13): 9781441928627
ISBN (ISBN-10): 1441928626
Hardcover
Paperback
Publishing year: 2010
Publisher: Springer New York
312 Pages
Weight: 0,465 kg
Language: eng/Englisch

Book in our database since 2011-03-08T22:23:28+00:00 (London)
Detail page last modified on 2024-02-27T07:08:20+00:00 (London)
ISBN/EAN: 9781441928627

ISBN - alternate spelling:
1-4419-2862-6, 978-1-4419-2862-7
Alternate spelling and related search-keywords:
Book author: steele
Book title: applications probability, applications application, financial modelling, applied calculus, stochastic calculus applications

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Information from Publisher

Author: J. Michael Steele
Title: Stochastic Modelling and Applied Probability; Stochastic Calculus and Financial Applications
Publisher: Springer; Springer US
302 Pages
Publishing year: 2010-12-01
New York; NY; US
Printed / Made in
Language: English
87,99 € (DE)

BC; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; Stochastic Differential Equations; Stochastic Processes; Stochastic calculus; Uniform integrability; Variance; calculus; statistics; quantitative finance; Probability Theory; Mathematics in Business, Economics and Finance; Statistical Theory and Methods; Stochastik; Angewandte Mathematik; Wirtschaftswissenschaft, Finanzen, Betriebswirtschaft und Management; BB; EA

1. Random Walk and First Step Analysis.- 1.1. First Step Analysis.- 1.2. Time and Infinity.- 1.3. Tossing an Unfair Coin.- 1.4. Numerical Calculation and Intuition.- 1.5. First Steps with Generating Functions.- 1.6. Exercises.- 2. First Martingale Steps.- 2.1. Classic Examples.- 2.2. New Martingales from Old.- 2.3. Revisiting the Old Ruins.- 2.4. Submartingales.- 2.5. Doob’s Inequalities.- 2.6. Martingale Convergence.- 2.7. Exercises.- 3. Brownian Motion.- 3.1. Covariances and Characteristic Functions.- 3.2. Visions of a Series Approximation.- 3.3. Two Wavelets.- 3.4. Wavelet Representation of Brownian Motion.- 3.5. Scaling and Inverting Brownian Motion.- 3.6. Exercises.- 4. Martingales: The Next Steps.- 4.1. Foundation Stones.- 4.2. Conditional Expectations.- 4.3. Uniform Integrability.- 4.4. Martingales in Continuous Time.- 4.5. Classic Brownian Motion Martingales.- 4.6. Exercises.- 5. Richness of Paths.- 5.1. Quantitative Smoothness.- 5.2. Not Too Smooth.- 5.3. Two Reflection Principles.- 5.4. The Invariance Principle and Donsker’s Theorem.- 5.5. Random Walks Inside Brownian Motion.- 5.6. Exercises.- 6. Itô Integration.- 6.1. Definition of the Ito Integral: First Two Steps.- 6.2. Third Step: Itô’s Integral as a Process.- 6.3. The Integral Sign: Benefits and Costs.- 6.4. An Explicit Calculation.- 6.5. Pathwise Interpretation of Ito Integrals.- 6.6. Approximation in H2.- 6.7. Exercises.- 7. Localization and Itô’s Integral.- 7.1. Itô’s Integral on L2LOC.- 7.2. An Intuitive Representation.- 7.3. Why Just L2LOC?.- 7.4. Local Martingales and Honest Ones.- 7.5. Alternative Fields and Changes of Time.- 7.6. Exercises.- 8. Itô’s Formula.- 8.1. Analysis and Synthesis.- 8.2. First Consequences and Enhancements.- 8.3. Vector Extension and Harmonic Functions.-8.4. Functions of Processes.- 8.5. The General Ito Formula.- 8.6. Quadratic Variation.- 8.7. Exercises.- 9. Stochastic Differential Equations.- 9.1. Matching Itô’s Coefficients.- 9.2. Ornstein-Uhlenbeck Processes.- 9.3. Matching Product Process Coefficients.- 9.4. Existence and Uniqueness Theorems.- 9.5. Systems of SDEs.- 9.6. Exercises.- 10. Arbitrage and SDEs.- 10.1. Replication and Three Examples of Arbitrage.- 10.2. The Black-Scholes Model.- 10.3. The Black-Scholes Formula.- 10.4. Two Original Derivations.- 10.5. The Perplexing Power of a Formula.- 10.6. Exercises.- 11. The Diffusion Equation.- 11.1. The Diffusion of Mice.- 11.2. Solutions of the Diffusion Equation.- 11.3. Uniqueness of Solutions.- 11.4. How to Solve the Black-Scholes PDE.- 11.5. Uniqueness and the Black-Scholes PDE.- 11.6. Exercises.- 12. Representation Theorems.- 12.1. Stochastic Integral Representation Theorem.- 12.2. The Martingale Representation Theorem.- 12.3. Continuity of Conditional Expectations.- 12.4. Lévy’s Representation Theorem.- 12.5. Two Consequences of Lévy’s Representation.- 12.6. Bedrock Approximation Techniques.- 12.7. Exercises.- 13. Girsanov Theory.- 13.1. Importance Sampling.- 13.2. Tilting a Process.- 13.3. Simplest Girsanov Theorem.- 13.4. Creation of Martingales.- 13.5. Shifting the General Drift.- 13.6. Exponential Martingales and Novikov’s Condition.- 13.7. Exercises.- 14. Arbitrage and Martingales.- 14.1. Reexamination of the Binomial Arbitrage.- 14.2. The Valuation Formula in Continuous Time.- 14.3. The Black-Scholes Formula via Martingales.- 14.4. American Options.- 14.5. Self-Financing and Self-Doubt.- 14.6. Admissible Strategies and Completeness.- 14.7. Perspective on Theory and Practice.- 14.8. Exercises.- 15. The Feynman-Kac Connection.- 15.1. FirstLinks.- 15.2. The Feynman-Kac Connection for Brownian Motion.- 15.3. Lévy’s Arcsin Law.- 15.4. The Feynman-Kac Connection for Diffusions.- 15.5. Feynman-Kac and the Black-Scholes PDEs.- 15.6. Exercises.- Appendix I. Mathematical Tools.- Appendix II. Comments and Credits.