Stochastic financial models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2010
|
| Series: | Chapman & Hall/CRC financial mathematics series
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 257 S. graph. Darst. |
| ISBN: | 9781420093452 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic financial models |c Douglas Kennedy |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2010 | |
| 300 | |a 257 S. |b graph. Darst. | ||
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| 650 | 4 | |a Investments |x Mathematical models | |
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Record in the Search Index
| _version_ | 1804141220986880000 |
|---|---|
| adam_text | Contents
Preface
ix
1 Portfolio
Choice
1
1.1
Introduction
.............................. 1
1.2
Utility
................................. 2
1.2.1
Preferences and utility
.................... 2
1.2.2
Utility and risk aversion
................... 7
1.3
Mean-variance analysis
........................ 9
1.3.1
Introduction
.......................... 9
1.3.2
All risky assets
........................ 9
1.3.3
A riskless asset
........................ 14
1.3.4
Mean-variance analysis and expected utility
......... 18
1.3.5
Equilibrium: the capital-asset pricing model
......... 19
1.4
Exercises
............................... 20
2
The Binomial Model
25
2.1
One-period model
.......................... 25
2.1.1
Introduction
.......................... 25
2.1.2
Hedging
............................ 26
2.1.3
Arbitrage
........................... 28
2.1.4
Utility maximization
..................... 29
2.2
Multi-period model
.......................... 31
2.2.1
Introduction
.......................... 31
2.2.2
Dynamic hedging
....................... 33
2.2.3
Change of probability
.................... 40
2.2.4
Utility maximization
..................... 42
2.2.5
Path-dependent claims
.................... 44
2.2.6
American claims
....................... 49
2.2.7
The non-standard multi-period model
............ 54
2.3
Exercises
............................... 59
3
A General Discrete-Time Model
63
3.1
One-period model
.......................... 63
3.1.1
Introduction
.......................... 63
3.1.2
Arbitrage
........................... 69
3.2
Multi-period model
.......................... 73
3.2.1
Introduction
.......................... 73
3.2.2
Pricing
claims
........................ 76
3.3
Exercises
............................... 81
Brownian Motion
83
4.1
Introduction
.............................. 83
4.2
Hitting-time distributions
....................... 85
4.2.1
The reflection principle
.................... 85
4.2.2
Transformations of Brownian motion
............ 93
4.2.3
Computations using martingales
............... 94
4.3
Girsanov s Theorem
......................... 97
4.4
Brownian motion as a limit
...................... 100
4.5
Stochastic calculus
.......................... 102
4.6
Exercises
............................... 109
The Black-Scholes Model
113
5.1
Introduction
.............................. 113
5.2
The Black-Scholes formula
..................... 114
5.2.1
Derivation
........................... 114
5.2.2
Dependence on the parameters: the Greeks
......... 116
5.2.3
Volatility
........................... 119
5.3
Hedging and the Black-Scholes equation
.............. 123
5.3.1
Self-financing portfolios
................... 123
5.3.2
Dividend-paying claims
................... 128
5.3.3
General terminal-value claims
................ 130
5.3.4
Specific terminal-value claims
................ 134
5.3.5
Utility maximization
..................... 137
5.3.6
American claims
....................... 143
5.4
Path-dependent claims
........................ 146
5.4.1
Forward-start and
lookback
options
............. 146
5.4.2
Barrier options
........................ 150
5.5
Dividend-paying assets
........................ 156
5.6
Exercises
............................... 159
Interest-Rate Models
165
6.1
Introduction
.............................. 165
6.2
Survey of interest-rate models
.................... 168
6.2.1
One-factor models
...................... 168
6.2.2
Forward-rate and market models
............... 172
6.3
Gaussian random-field model
.................... 174
6.3.1
Introduction
.......................... 174
6.3.2
Pricing a caplet on forward rates
............... 178
6.3.3
Markov properties
...................... 182
6.3.4
Finite-factor models and restricted information
....... 188
6.4
Exercises
............................... 190
A Mathematical Preliminaries
193
A.I Probability background
........................ 193
АЛЛ
Probability spaces
...................... 193
A.
1.2
Conditional expectations
................... 194
АЛ.З
Change of probability
.................... 194
АЛ.4
Essential supremum
..................... 196
A.2 Martingales
.............................. 196
A.3 Gaussian random variables
...................... 198
А.ЗЛ
Univariate normal distributions
................ 198
A.3.2 Multivariate normal distributions
............... 200
A.4 Convexity
............................... 204
В
Solutions to the Exercises
207
ВЛ
Portfolio Choice
........................... 207
B.2 The Binomial Model
......................... 213
B.3 A General Discrete-Time Model
................... 221
B.4 Brownian Motion
........................... 226
B.5 The Black-Scholes Model
...................... 231
B.6 Interest-Rate Models
......................... 240
Further Reading
247
References
249
Index
253
|
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| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.63/2042 |
| dewey-search | 332.63/2042 |
| dewey-sort | 3332.63 42042 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV036117047 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:12:25Z |
| institution | BVB |
| isbn | 9781420093452 |
| language | English |
| lccn | 2009044114 |
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| owner_facet | DE-355 DE-BY-UBR DE-634 DE-824 DE-19 DE-BY-UBM |
| physical | 257 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman & Hall/CRC financial mathematics series A Chapman & Hall book |
| spelling | Kennedy, Douglas Verfasser aut Stochastic financial models Douglas Kennedy Boca Raton [u.a.] CRC Press 2010 257 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series A Chapman & Hall book Mathematisches Modell Investments Mathematical models Stochastic analysis Portfolio Selection (DE-588)4046834-3 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Portfolio Selection (DE-588)4046834-3 s Finanzmathematik (DE-588)4017195-4 s Stochastisches Modell (DE-588)4057633-4 s b DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019007132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kennedy, Douglas Stochastic financial models Mathematisches Modell Investments Mathematical models Stochastic analysis Portfolio Selection (DE-588)4046834-3 gnd Finanzmathematik (DE-588)4017195-4 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4046834-3 (DE-588)4017195-4 (DE-588)4057633-4 |
| title | Stochastic financial models |
| title_auth | Stochastic financial models |
| title_exact_search | Stochastic financial models |
| title_full | Stochastic financial models Douglas Kennedy |
| title_fullStr | Stochastic financial models Douglas Kennedy |
| title_full_unstemmed | Stochastic financial models Douglas Kennedy |
| title_short | Stochastic financial models |
| title_sort | stochastic financial models |
| topic | Mathematisches Modell Investments Mathematical models Stochastic analysis Portfolio Selection (DE-588)4046834-3 gnd Finanzmathematik (DE-588)4017195-4 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Mathematisches Modell Investments Mathematical models Stochastic analysis Portfolio Selection Finanzmathematik Stochastisches Modell |
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