Atnaujinkite slapukų nuostatas

Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach [Kietas viršelis]

4.33/5 (3 ratings by Goodreads)
, ,
  • Formatas: Hardback, 752 pages, aukštis x plotis x storis: 243x161x43 mm, weight: 1111 g
  • Išleidimo metai: 13-May-2014
  • Leidėjas: John Wiley & Sons Inc
  • ISBN-10: 1118831969
  • ISBN-13: 9781118831960
Kitos knygos pagal šią temą:
Measure, Probability, and Mathematical Finance: A Problem-Oriented ApproachDidesnis paveikslėlis
  • Formatas: Hardback, 752 pages, aukštis x plotis x storis: 243x161x43 mm, weight: 1111 g
  • Išleidimo metai: 13-May-2014
  • Leidėjas: John Wiley & Sons Inc
  • ISBN-10: 1118831969
  • ISBN-13: 9781118831960
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781118831960.html
Raktažodžiai:
Providing the mathematical theory needed to understand the financial models of Wall Street, this book covers the basic concepts and the important theorems of mathematical finance and provides plenty of illustrative problems for reinforcement, with hints and solutions. A sampling of topics: sets and sequences, Lebesgue-Stieltjes measures, the Radon-Nikodym theorem, events and random variables, discrete and continuous distributions, and various topics related to stochastic calculus and financial models. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

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 LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models.

The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features:

  • A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus
  • Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems
  • Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes
Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.
Preface xvii
Financial Glossary xxii
Part I Measure Theory
1 Sets and Sequences
3(12)
1.1 Basic Concepts and Facts
3(3)
1.2 Problems
6(2)
1.3 Hints
8(1)
1.4 Solutions
8(5)
1.5 Bibliographic Notes
13(2)
2 Measures
15(14)
2.1 Basic Concepts and Facts
15(3)
2.2 Problems
18(2)
2.3 Hints
20(1)
2.4 Solutions
21(7)
2.5 Bibliographic Notes
28(1)
3 Extension of Measures
29(8)
3.1 Basic Concepts and Facts
29(1)
3.2 Problems
30(2)
3.3 Hints
32(1)
3.4 Solutions
32(4)
3.5 Bibliographic Notes
36(1)
4 Lebesgue-Stieltjes Measures
37(10)
4.1 Basic Concepts and Facts
37(2)
4.2 Problems
39(2)
4.3 Hints
41(1)
4.4 Solutions
41(4)
4.5 Bibliographic Notes
45(2)
5 Measurable Functions
47(10)
5.1 Basic Concepts and Facts
47(1)
5.2 Problems
48(2)
5.3 'Hints
50(1)
5.4 Solutions
51(5)
5.5 Bibliographic Notes
56(1)
6 Lebesgue Integration
57(20)
6.1 Basic Concepts and Facts
57(2)
6.2 Problems
59(3)
6.3 Hints
62(2)
6.4 Solutions
64(12)
6.5 Bibliographic Notes
76(1)
7 The Radon-Nikodym Theorem
77(8)
7.1 Basic Concepts and Facts
77(2)
7.2 Problems
79(1)
7.3 Hints
80(1)
7.4 Solutions
80(3)
7.5 Bibliographic Notes
83(2)
8 LP Spaces
85(12)
8.1 Basic Concepts and Facts
85(3)
8.2 Problems
88(1)
8.3 Hints
89(1)
8.4 Solutions
90(5)
8.5 Bibliographic Notes
95(2)
9 Convergence
97(16)
9.1 Basic Concepts and Facts
97(1)
9.2 Problems
98(2)
9.3 Hints
100(2)
9.4 Solutions
102(9)
9.5 Bibliographic Notes
111(2)
10 Product Measures
113(14)
10.1 Basic Concepts and Facts
113(2)
10.2 Problems
115(3)
10.3 Hints
118(1)
10.4 Solutions
118(5)
10.5 Bibliographic Notes
123(4)
Part II Probability Theory
11 Events and Random Variables
127(14)
11.1 Basic Concepts and Facts
127(3)
11.2 Problems
130(2)
11.3 Hints
132(1)
11.4 Solutions
133(6)
11.5 Bibliographic Notes
139(2)
12 Independence
141(20)
12.1 Basic Concepts and Facts
141(1)
12.2 Problems
142(3)
12.3 Hints
145(1)
12.4 Solutions
146(13)
12.5 Bibliographic Notes
159(2)
13 Expectation
161(12)
13.1 Basic Concepts and Facts
161(2)
13.2 Problems
163(2)
13.3 Hints
165(1)
13.4 Solutions
166(6)
13.5 Bibliographic Notes
172(1)
14 Conditional Expectation
173(16)
14.1 Basic Concepts and Facts
173(2)
14.2 Problems
175(3)
14.3 Hints
178(1)
14.4 Solutions
179(8)
14.5 Bibliographic Notes
187(2)
15 Inequalities
189(10)
15.1 Basic Concepts and Facts
189(1)
15.2 Problems
190(1)
15.3 Hints
191(1)
15.4 Solutions
192(6)
15.5 Bibliographic Notes
198(1)
16 Law of Large Numbers
199(18)
16.1 Basic Concepts and Facts
199(1)
16.2 Problems
200(3)
16.3 Hints
203(2)
16.4 Solutions
205(10)
16.5 Bibliographic Notes
215(2)
17 Characteristic Functions
217(10)
17.1 Basic Concepts and Facts
217(1)
17.2 Problems
218(2)
17.3 Hints
220(1)
17.4 Solutions
221(5)
17.5 Bibliographic Notes
226(1)
18 Discrete Distributions
227(12)
18.1 Basic Concepts and Facts
227(1)
18.2 Problems
228(2)
18.3 Hints
230(1)
18.4 Solutions
231(6)
18.5 Bibliographic Notes
237(2)
19 Continuous Distributions
239(18)
19.1 Basic Concepts and Facts
239(2)
19.2 Problems
241(3)
19.3 Hints
244(2)
19.4 Solutions
246(10)
19.5 Bibliographic Notes
256(1)
20 Central Limit Theorems
257(14)
20.1 Basic Concepts and Facts
257(1)
20.2 Problems
258(2)
20.3 Hints
260(1)
20.4 Solutions
261(6)
20.5 Bibliographic Notes
267(4)
Part III Stochastic Processes
21 Stochastic Processes
271(20)
21.1 Basic Concepts and Facts
271(4)
21.2 Problems
275(3)
21.3 Hints
278(2)
21.4 Solutions
280(9)
21.5 Bibliographic Notes
289(2)
22 Martingales
291(10)
22.1 Basic Concepts and Facts
291(1)
22.2 Problems
292(2)
22.3 Hints
294(1)
22.4 Solutions
295(5)
22.5 Bibliographic Notes
300(1)
23 Stopping Times
301(20)
23.1 Basic Concepts and Facts
301(2)
23.2 Problems
303(2)
23.3 Hints
305(2)
23.4 Solutions
307(12)
23.5 Bibliographic Notes
319(2)
24 Martingale Inequalities
321(12)
24.1 Basic Concepts and Facts
321(1)
24.2 Problems
322(1)
24.3 Hints
323(1)
24.4 Solutions
324(7)
24.5 Bibliographic Notes
331(2)
25 Martingale Convergence Theorems
333(10)
25.1 Basic Concepts and Facts
333(1)
25.2 Problems
334(2)
25.3 Hints
336(1)
25.4 Solutions
336(6)
25.5 Bibliographic Notes
342(1)
26 Random Walks
343(14)
26.1 Basic Concepts and Facts
343(1)
26.2 Problems
344(2)
26.3 Hints
346(1)
26.4 Solutions
347(8)
26.5 Bibliographic Notes
355(2)
27 Poisson Processes
357(16)
27.1 Basic Concepts and Facts
357(2)
27.2 Problems
359(2)
27.3 Hints
361(1)
27.4 Solutions
361(10)
27.5 Bibliographic Notes
371(2)
28 Brownian Motion
373(16)
28.1 Basic Concepts and Facts
373(2)
28.2 Problems
375(2)
28.3 Hints
377(1)
28.4 Solutions
378(9)
28.5 Bibliographic Notes
387(2)
29 Markov Processes
389(12)
29.1 Basic Concepts and Facts
389(2)
29.2 Problems
391(2)
29.3 Hints
393(1)
29.4 Solutions
394(5)
29.5 Bibliographic Notes
399(2)
30 Levy Processes
401(20)
30.1 Basic Concepts and Facts
401(3)
30.2 Problems
404(3)
30.3 Hints
407(1)
30.4 Solutions
408(9)
30.5 Bibliographic Notes
417(4)
Part IV Stochastic Calculus
31 The Wiener Integral
421(10)
31.1 Basic Concepts and Facts
421(2)
31.2 Problems
423(1)
31.3 flints
424(1)
31.4 Solutions
425(4)
31.5 Bibliographic Notes
429(2)
32 The Ito Integral
431(22)
32.1 Basic Concepts and Facts
431(2)
32.2 Problems
433(4)
32.3 Hints
437(1)
32.4 Solutions
438(14)
32.5 Bibliographic Notes
452(1)
33 Extension of the Ito Integral
453(10)
33.1 Basic Concepts and Facts
453(2)
33.2 Problems
455(1)
33.3 Hints
456(1)
33.4 Solutions
457(5)
33.5 Bibliographic Notes
462(1)
34 Martingale Stochastic Integrals
463(14)
34.1 Basic Concepts and Facts
463(5)
34.2 Problems
468(1)
34.3 Hints
469(1)
34.4 Solutions
470(5)
34.5 Bibliographic Notes
475(2)
35 The Ito Formula
477(18)
35.1 Basic Concepts and Facts
477(4)
35.2 Problems
481(2)
35.3 Hints
483(2)
35.4 Solutions
485(9)
35.5 Bibliographic Notes
494(1)
36 Martingale Representation Theorem
495(8)
36.1 Basic Concepts and Facts
495(1)
36.2 Problems
496(1)
36.3 Hints
497(1)
36.4 Solutions
498(3)
36.5 Bibliographic Notes
501(2)
37 Change of Measure
503(12)
37.1 Basic Concepts and Facts
503(1)
37.2 Problems
504(4)
37.3 Hints
508(1)
37.4 Solutions
508(5)
37.5 Bibliographic Notes
513(2)
38 Stochastic Differential Equations
515(16)
38.1 Basic Concepts and Facts
515(2)
38.2 Problems
517(4)
38.3 Hints
521(1)
38.4 Solutions
522(8)
38.5 Bibliographic Notes
530(1)
39 Diffusion
531(16)
39.1 Basic Concepts and Facts
531(3)
39.2 Problems
534(2)
39.3 Hints
536(1)
39.4 Solutions
537(8)
39.5 Bibliographic Notes
545(2)
40 The Feynman-Kac Formula
547(14)
40.1 Basic Concepts and Facts
547(2)
40.2 Problems
549(2)
40.3 Hints
551(1)
40.4 Solutions
552(5)
40.5 Bibliographic Notes
557(4)
Part V Stochastic Financial Models
41 Discrete-Time Models
561(18)
41.1 Basic Concepts and Facts
561(4)
41.2 Problems
565(3)
41.3 Hints
568(1)
41.4 Solutions
569(7)
41.5 Bibliographic Notes
576(3)
42 Black-Scholes Option Pricing Models
579(14)
42.1 Basic Concepts and Facts
579(4)
42.2 Problems
583(2)
42.3 Hints
585(1)
42.4 Solutions
586(5)
42.5 Bibliographic Notes
591(2)
43 Path-Dependent Options
593(16)
43.1 Basic Concepts and Facts
593(5)
43.2 Problems
598(2)
43.3 Hints
600(1)
43.4 Solutions
601(7)
43.5 Bibliographic Notes
608(1)
44 American Options
609(20)
44.1 Basic Concepts and Facts
609(4)
44.2 Problems
613(3)
44.3 Hints
616(1)
44.4 Solutions
617(9)
44.5 Bibliographic Notes
626(3)
45 Short Rate Models
629(18)
45.1 Basic Concepts and Facts
629(2)
45.2 Problems
631(4)
45.3 Hints
635(1)
45.4 Solutions
635(9)
45.5 Bibliographic Notes
644(3)
46 Instantaneous Forward Rate Models
647(20)
46.1 Basic Concepts and Facts
647(3)
46.2 Problems
650(4)
46.3 Hints
654(1)
46.4 Solutions
654(11)
46.5 Bibliographic Notes
665(2)
47 LIBOR Market Models
667(20)
47.1 Basic Concepts and Facts
667(1)
47.2 Problems
668(4)
47.3 Hints
672(1)
47.4 Solutions
673(12)
47.5 Bibliographic Notes
685(2)
References 687(16)
List of Symbols 703(4)
Subject Index 707
GUOJUN GAN, PHD, ASA, is Director of Quantitative Modeling and Model Efficiency at Manulife Financial, Canada. His research interests include empirical corporate finance, actuarial science, risk management, data mining, and big data analysis.

CHAOQUN MA, PHD, is Professor and Dean of the School of Business Administration at Hunan University, China. The recipient of First Prize in Outstanding Achievements in Teaching in 2009, Dr. Mas research interests include financial engineering, risk management, and data mining.

HONG XIE, PHD, is Adjunct Professor in the Department of Mathematics and Statistics at York University as well as Vice President of Models and Analytics at Manulife Financial, Canada. Dr. Xie is on the Board of Directors for the Canadian-Chinese Finance Association, and his research interests include financial engineering, mathematical finance, and partial differential equations.