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Viser: Stochastic Calculus and Applications
Stochastic Calculus and Applications Vital Source e-bog
Samuel N. Cohen og Robert J. Elliott
(2015)
Stochastic Calculus and Applications
Robert J. Elliott og Samuel N. Cohen
(2015)
Sprog: Engelsk
Detaljer om varen
- 2. Udgave
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Springer Nature (November 2015)
- Forfattere: Samuel N. Cohen og Robert J. Elliott
- ISBN: 9781493928675
Bookshelf online: 5 år fra købsdato.
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Detaljer om varen
- 2. Udgave
- Hardback
- Udgiver: Springer New York (November 2015)
- Forfattere: Robert J. Elliott og Samuel N. Cohen
- ISBN: 9781493928668
Revised and expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes as used by systems theorists, electronic engineers and, more recently, those working in quantitative, mathematical finance.Building upon the original release of this title it will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry.
New features ofthisedition include:
End of chapter exercises; New chapters on basic measure theory and Backward SDEs;- Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index.
"Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."-Zentralblatt (from review of the First Edition)
"
Part I: Measure Theoretic Probability.- Measure Integral.- Probabilities and Expectation.-
Part II: Stochastic Processes.- Filtrations, Stopping Times and Stochastic Processes.- Martingales in Discrete Time.- Martingales in Continuous Time.- The Classification of Stopping Times.- The Progressive, Optional and Predicable -Algebras.-
Part III: Stochastic Integration.- Processes of Finite Variation.- The Doob-Meyer Decomposition.- The Structure of Square Integrable Martingales.- Quadratic Variation and Semimartingales.- The Stochastic Integral.- Random Measures.-
Part IV: Stochastic Differential Equations.- Ito's Differential Rule.- The Exponential Formula and Girsanov's Theorem.- Lipschitz Stochastic Differential Equations.- Markov Properties of SDEs.- Weak Solutions of SDEs.- Backward Stochastic Differential Equations.-
Part V: Applications.- Control of a Single Jump.- Optimal Control of Drifts and Jump Rates.- Filtering.
Part VI: Appendices.
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