Measure, probability, and mathematical finance : a problem-oriented approach / Guojun Gan, Chaoqun Ma and Hong Xie.
Material type:
TextPublication details: New Jersey : John Wiley, c2014.Description: xxiii, 715 p. ; 25 cmISBN: - 9781118831960 (cloth)
- 23 G195 000SB:332
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 000SB:332 G195 (Browse shelf(Opens below)) | Available | 135595 |
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| 000SB:332 F829 Statistics of financial markets | 000SB:332 F829 Statistics of financial markets | 000SB:332 F829 Statistics of financial markets : an introduction / | 000SB:332 G195 Measure, probability, and mathematical finance : a problem-oriented approach / | 000SB:332 G716 ARCH models and financial applications | 000SB:332 G716 ARCH models and financial applications | 000SB:332 G821 Financial econometrics modeling |
Includes bibliographical references and indexes.
Part I Measure theory --
1. Sets and sequences --
2. Measures --
3. Extension of measures --
4. Lebesgue Stieltjee measures --
5. Measurable functions --
6. Lebesgue integration --
7. The Radon Nikodym theorem --
8. LP spaces --
9. Convergence --
10. Product measures --
Part II Probability theory --
11. Events and random variables --
12. Independence --
13. Expectation --
14. Conditional expectation --
15. Inequalities --
16. Law of large numbers --
17. Characteristic functions --
18. Discrete distributions --
19. Continuous distributions --
20. Central limit theorems --
Part III. Stochastic processes --
21. Stochastic processes --
22. Martingales --
23. Stopping times --
24. Martingale inequalities --
25. Martingale convergence theorems --
26. Random walks --
27. Poisson processes --
28. Brownian motions --
29. Markov processes --
30. Levy processes --
Part IV. Stochastic calculus --
31. The wiener integral --
32. The it "o" integral --
33. Extension of it "o" integrals --
34. Martingale stochastic integrals --
35. The it o's formula --
36. Martingale representation theorem --
37. Change of measure --
38. Stochastic differential equations --
39. Diffusions --
40. The Feyn Mankac formula --
Part V. Stochastic financial models --
41. Discrete-time models --
42. Black-scholes option pricing models --
43. Path-dependent options --
44. American options --
45. Short rate models--
46. Instantaneous forward rate models --
47. LIBOR market models--
References --
List of symbols --
Subject index --
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 numeraire theory, and LI.
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