Change of time and change of measure:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2010
|
| Schriftenreihe: | Advanced series on statistical science & applied probability
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 291-300) and index |
| Beschreibung: | XVI, 305 S. 24 cm |
| ISBN: | 9789814324472 9814324477 |
Internformat
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| 100 | 1 | |a Barndorff-Nielsen, Ole E. |d 1935- |e Verfasser |0 (DE-588)123060915 |4 aut | |
| 245 | 1 | 0 | |a Change of time and change of measure |c Ole E. Barndorff-Nielsen ; Albert Shiryaev |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2010 | |
| 300 | |a XVI, 305 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Advanced series on statistical science & applied probability |v 13 | |
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Datensatz im Suchindex
| _version_ | 1804148339337330688 |
|---|---|
| adam_text | Titel: Change of time and change of measure
Autor: Barndorff-Nielsen, Ole E
Jahr: 2010
Contents
Foreword v
Introduction xi
1. Random Change of Time 1
1.1 Basic Definitions....................... 1
1.2 Some Properties of Change of Time ............ 4
1.3 Representations in the Weak Sense (X = XoT), in the
Strong Sense (X = XoT) and the Semi-strong Sense (X a=
XoT). I. Constructive Examples.............. 8
1.4 Representations in the Weak Sense (X = XoT), Strong
Sense (X = X o T) and the Semi-strong Sense (X =
XoT). II. The Case of Continuous Local Martingales and
Processes of Bounded Variation............... 15
2. Integral Representations and Change of Time in Stochas-
tic Integrals 25
2.1 Integral Representations of Local Martingales in the Strong
Sense.............................. 25
2.2 Integral Representations of Local Martingales in a Semi-
strong Sense.......................... 33
2.3 Stochastic Integrals Over the Stable Processes and Integral
Representations........................ 35
2.4 Stochastic Integrals with Respect to Stable Processes and
Change of Time........................ 38
3. Semimartingales: Basic Notions, Structures, Elements of
vi;; Contents
Stochastic Analysis 41
3.1 Basic Definitions and Properties.............. 41
3.2 Canonical Representation. Triplets of Predictable Charac-
teristics ............................ 52
3.3 Stochastic Integrals with Respect to a Brownian Motion,
Square-integrable Martingales, and Semiinartingalcs ... 56
3.4 Stochastic Differential Equations.............. 73
4. Stochastic Exponential and Stochastic Logarithm. Cu-
mulant Processes 91
4.1 Stochastic Exponential and Stochastic Logarithm..... 91
4.2 Fourier Cumulant Processes................. 90
4.3 Laplace Cumulant Processes................. 99
4.4 Cumulant Processes of Stochastic Integral Transformation
X* = p-X.......................... 101
5. Processes with Independent Increments. Levy Processes 105
5.1 Processes with Independent Increments and
Semimartingales....................... 105
5.2 Processes with Stationary Independent Increments (Levy
Processes)........................... 108
5.3 Some Properties of Sample Paths of Processes with Inde-
pendent Increments...................... 113
5.4 Some Properties of Sample Paths of Processes with Sta-
tionary Independent Increments (Levy Processes)..... 117
6. Change of Measure. General Facts 121
6.1 Basic Definitions. Density Process............. 121
6.2 Discrete Version of Girsanov s Theorem.......... 123
6.3 Semimartingale Version of Girsanov s Theorem...... 126
6.4 Esscher s Change of Measure................ 132
7. Change of Measure in Models Based on Levy Processes 135
7.1 Linear and Exponential Levy Models under Change of
Measure............................ 135
7.2 On the Criteria of Local Absolute Continuity of Two Mea-
sures of Levy Processes ................... 142
Contents ix
7.3 On the Uniqueness of Locally Equivalent Martingale-type
Measures for the Exponential Levy Models ........ 144
7.4 On the Construction of Martingale Measures with Minimal
Entropy in the Exponential Levy Models.......... 147
8. Change of Time in Semimartingale Models and Models
Based on Brownian Motion and Levy Processes 151
8.1 Some General Facts about Change of Time for Semimar-
tingale Models ........................ 151
8.2 Change of Time in Brownian Motion. Different Formu-
lations ............................. 154
8.3 Change of Time Given by Subordinators. I. Some Ex-
amples ............................. 156
8.4 Change of Time Given by Subordinators. II. Structure of
the Triplets of Predictable Characteristics......... 158
9. Conditionally Gaussian Distributions and Stochastic
Volatility Models for the Discrete-time Case 163
9.1 Deviation from the Gaussian Property of the Returns of
the Prices........................... 163
9.2 Martingale Approach to the Study of the Returns of the
Prices............................. 166
9.3 Conditionally Gaussian Models. I. Linear (AR, MA,
ARMA) and Nonlinear (ARCH, GARCH) Models for
Returns............................ 171
9.4 Conditionally Gaussian Models. II. IG- and GIG-
distributions for the Square of Stochastic Volatility and
GH-distributions for Returns................ 175
10. Martingale Measures in the Stochastic Theory of Arbitrage 195
10.1 Basic Notions and Summary of Results of the Theory of
Arbitrage. I. Discrete Time Models............. 195
10.2 Basic Notions and Summary of Results of the Theory of
Arbitrage. II. Continuous-Time Models .......... 207
10.3 Arbitrage in a Model of Buying/Selling Assets with Trans-
action Costs.......................... 215
10.4 Asymptotic Arbitrage: Some Problems........... 216
11. Change of Measure in Option Pricing 225
x Contents
11.1 Overview of the Pricing Formulae for European Options . 225
11.2 Overview of the Pricing Formulae for American Options . 240
11.3 Duality and Symmetry of the Semimartingale Models .. 243
11.4 Call-Put Duality in Option Pricing. Levy Models..... 254
12. Conditionally Brownian and Levy Processes. Stochastic
Volatility Models 259
12.1 From Black-Scholes Theory of Pricing of Derivatives to
the Implied Volatility, Smile Effect and Stochastic Volatil-
ity Models........................... 259
12.2 Generalized Inverse Gaussian Subordinator and General-
ized Hyperbolic Levy Motion: Two Methods of Construc-
tion, Sample Path Properties................ 270
12.3 Distributional and Sample-path Properties of the Levy
Processes L(GIG) and L(GH)................ 275
12.4 On Some Others Models of the Dynamics of Prices. Com-
parison of the Properties of Different Models ....... 283
Afterword 289
Bibliography 291
Index 301
|
| any_adam_object | 1 |
| author | Barndorff-Nielsen, Ole E. 1935- Širjaev, Alʹbert N. 1934- |
| author_GND | (DE-588)123060915 (DE-588)12203502X |
| author_facet | Barndorff-Nielsen, Ole E. 1935- Širjaev, Alʹbert N. 1934- |
| author_role | aut aut |
| author_sort | Barndorff-Nielsen, Ole E. 1935- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| language | English |
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| series2 | Advanced series on statistical science & applied probability |
| spelling | Barndorff-Nielsen, Ole E. 1935- Verfasser (DE-588)123060915 aut Change of time and change of measure Ole E. Barndorff-Nielsen ; Albert Shiryaev Singapore [u.a.] World Scientific 2010 XVI, 305 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science & applied probability 13 Includes bibliographical references (p. 291-300) and index Stochastic processes Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Diskreter stochastischer Prozess (DE-588)4150187-1 gnd rswk-swf Stetigkeit (DE-588)4183167-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Diskreter stochastischer Prozess (DE-588)4150187-1 s Stetigkeit (DE-588)4183167-6 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Lévy-Prozess (DE-588)4463623-4 s b DE-604 Širjaev, Alʹbert N. 1934- Verfasser (DE-588)12203502X aut Advanced series on statistical science & applied probability 13 (DE-604)BV011932321 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barndorff-Nielsen, Ole E. 1935- Širjaev, Alʹbert N. 1934- Change of time and change of measure Advanced series on statistical science & applied probability Stochastic processes Lévy-Prozess (DE-588)4463623-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Diskreter stochastischer Prozess (DE-588)4150187-1 gnd Stetigkeit (DE-588)4183167-6 gnd |
| subject_GND | (DE-588)4463623-4 (DE-588)4057630-9 (DE-588)4079013-7 (DE-588)4150187-1 (DE-588)4183167-6 |
| title | Change of time and change of measure |
| title_auth | Change of time and change of measure |
| title_exact_search | Change of time and change of measure |
| title_full | Change of time and change of measure Ole E. Barndorff-Nielsen ; Albert Shiryaev |
| title_fullStr | Change of time and change of measure Ole E. Barndorff-Nielsen ; Albert Shiryaev |
| title_full_unstemmed | Change of time and change of measure Ole E. Barndorff-Nielsen ; Albert Shiryaev |
| title_short | Change of time and change of measure |
| title_sort | change of time and change of measure |
| topic | Stochastic processes Lévy-Prozess (DE-588)4463623-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Diskreter stochastischer Prozess (DE-588)4150187-1 gnd Stetigkeit (DE-588)4183167-6 gnd |
| topic_facet | Stochastic processes Lévy-Prozess Stochastischer Prozess Wahrscheinlichkeitstheorie Diskreter stochastischer Prozess Stetigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024380615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932321 |
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