Stochastic processes with applications to finance:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2003
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 274 S. graph. Darst. |
| ISBN: | 1584882247 9781584882244 |
Staff View
MARC
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| 100 | 1 | |a Kijima, Masaaki |d 1957- |e Verfasser |0 (DE-588)124169015 |4 aut | |
| 245 | 1 | 0 | |a Stochastic processes with applications to finance |c Masaaki Kijima |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b Chapman & Hall/CRC |c 2003 | |
| 300 | |a XI, 274 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Matemática financeira |2 larpcal | |
| 650 | 7 | |a Mathématique financière |2 rasuqam | |
| 650 | 4 | |a Mathématiques financières | |
| 650 | 7 | |a Portfolio-theorie |2 gtt | |
| 650 | 7 | |a Processos estocasticos |2 larpcal | |
| 650 | 7 | |a Processus stochastique |2 rasuqam | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Business mathematics | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804139296563658752 |
|---|---|
| adam_text | Contents
Preface
v
1
Elementary Calculus: Towards Ito s Formula
1
1.1
Exponential and Logarithmic Functions
1
1.2
Differentiation
4
1.3
Taylor s Expansion
8
1.4
Ito s Formula
10
1.5
Integration
11
1.6
Exercises
15
2
Elements in Probability
19
2.1
The Sample Space and Probability
19
2.2
Discrete Random Variables
21
2.3
Continuous Random Variables
23
2.4
Multivariate Random Variables
25
2.5
Expectation
28
2.6
Conditional Expectation
32
2.7
Moment Generating Functions
35
2.8
Exorcises
37
3
Useful Distributions in Finance
41
3.1
Binomial Distributions
41
3.2
Other Discrete Distributions
43
3.3
Normal and Log-Normal Distributions
46
3.4
Other Continuous Distributions
50
3.5
Multivariate Normal Distributions
53
3.6
Exercises
57
4
Derivative Securities
61
4.1
The Money-Market Account
61
4.2
Various Interest Rates
62
4.3
Forward and Futures Contracts
66
4.4
Options
68
4.5
Interest-Rate Derivatives
70
4.6
Exercises
73
χ
CONTENTS
5
A Discrete-Time Model for Securities Market
75
5.1
Price Processes
75
5.2
The Portfolio Value and Stochastic Integral
78
5.3
No-Arbitrage and Replicating Portfolios
80
5.4
Martingales and the Asset Pricing Theorem
84
5.5
American Options
88
5.6
Change of Measure
90
5.7
Exercises
92
6
Random Walks
95
6.1
The Mathematical Definition
95
6.2
Transition Probabilities
96
6.3
The Reflection Principle
99
6.4
The Change of Measure Revisited
102
6.5
The Binomial Securities Market Model
105
6.6
Exercises
108
7
The Binomial Model 111
7.1
The Single-Period Mode! Ill
7.2
The
Multi-
Period Model
114
7.3
The Binomial Model for American Options
118
7.4
The Trinomial Model
119
7.5
The Binomial Model for Interest-Rate Claims
121
7.6
Exercises
124
8
A Discrete-Time Model for Defaultable Securities
127
8.1
The Hazard Rate
127
8.2
A Discrete Hazard Model
129
8.3
Pricing of Defaultable Securities
131
8.4
Correlated Defaults
135
8.5
Exercises
138
9
Markov Chains
141
9.1
Markov and Strong Markov Properties
141
9.2
Transition Probabilities
142
9.3
Absorbing Markov Chains
145
9.4
Applications to Finance
148
9.5
Exercises
154
10
Monte Carlo Simulation
157
10.1
Mathematical Backgrounds
157
10.2
The Idea of Monte Carlo
159
10.3
Generation of Random Numbers
162
10.4
Some Examples from Financial Engineering
165
10.5
Variance Reduction Methods
169
10.6
Exercises
172
CONTENTS xi
11
From Discrete to Continuous: Towards the Black—Scholes
175
11.1
Brownian Motions
175
11.2
The Central Limit Theorem Revisited
178
11.3
The Black-Scholes Formula
181
11.4
More on Brownian Motions
183
11.5
Poisson
Processes
187
11.6
Exercises
190
12
Basic Stochastic Processes in Continuous Time
193
12.1
Diffusion Processes
193
12.2
Sample Paths of Brownian Motions
197
12.3
Martingales
199
12.4
Stochastic Integrals
202
12.5
Stochastic Differential Equations
205
12.6
Ito s Formula Revisited
208
12.7
Exercises
211
13
A Continuous-Time Model for Securities Market
215
13.1
Self-Financing Portfolio and No-Arbitrage
215
13.2
Price Process Models
217
13.3
The Black-Scholes Model
222
13.4
The Risk-Neutral Method
225
13.5
The Forward-Neutral Method
231
13.6
The Interest-Rate Term Structure
234
13.7
Pricing of Interest-Rate Derivatives
241
13.8
Pricing of Corporate Debts
245
13.9
Exercises
253
References
261
Index
265
|
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| isbn | 1584882247 9781584882244 |
| language | English |
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| spelling | Kijima, Masaaki 1957- Verfasser (DE-588)124169015 aut Stochastic processes with applications to finance Masaaki Kijima Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2003 XI, 274 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Matemática financeira larpcal Mathématique financière rasuqam Mathématiques financières Portfolio-theorie gtt Processos estocasticos larpcal Processus stochastique rasuqam Processus stochastiques Stochastische processen gtt Stochastic processes Business mathematics Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Stochastischer Prozess (DE-588)4057630-9 s Finanzmathematik (DE-588)4017195-4 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017679283&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kijima, Masaaki 1957- Stochastic processes with applications to finance Matemática financeira larpcal Mathématique financière rasuqam Mathématiques financières Portfolio-theorie gtt Processos estocasticos larpcal Processus stochastique rasuqam Processus stochastiques Stochastische processen gtt Stochastic processes Business mathematics Stochastischer Prozess (DE-588)4057630-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4017195-4 (DE-588)1071861417 |
| title | Stochastic processes with applications to finance |
| title_auth | Stochastic processes with applications to finance |
| title_exact_search | Stochastic processes with applications to finance |
| title_full | Stochastic processes with applications to finance Masaaki Kijima |
| title_fullStr | Stochastic processes with applications to finance Masaaki Kijima |
| title_full_unstemmed | Stochastic processes with applications to finance Masaaki Kijima |
| title_short | Stochastic processes with applications to finance |
| title_sort | stochastic processes with applications to finance |
| topic | Matemática financeira larpcal Mathématique financière rasuqam Mathématiques financières Portfolio-theorie gtt Processos estocasticos larpcal Processus stochastique rasuqam Processus stochastiques Stochastische processen gtt Stochastic processes Business mathematics Stochastischer Prozess (DE-588)4057630-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Matemática financeira Mathématique financière Mathématiques financières Portfolio-theorie Processos estocasticos Processus stochastique Processus stochastiques Stochastische processen Stochastic processes Business mathematics Stochastischer Prozess Finanzmathematik Konferenzschrift |
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