Change of time and change of measure:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2015
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Advanced series on statistical science & applied probability
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 309-320) and index |
| Beschreibung: | XVIII, 326 S. 24 cm |
| ISBN: | 9789814678582 |
Internformat
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| 245 | 1 | 0 | |a Change of time and change of measure |c Ole E. Barndorff-Nielsen ; Albert Shiryaev |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2015 | |
| 300 | |a XVIII, 326 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Advanced series on statistical science & applied probability |v 21 | |
| 500 | |a Includes bibliographical references (p. 309-320) and index | ||
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Datensatz im Suchindex
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| adam_text | Contents
Foreword to the Second, Edition v
Foreword vii
Introduction xiii
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 l^= X o T), in the
Strong Sense (X = XoT) and the Semi-strong Sense (X
X oT). I. Constructive Examples........................... 8
1.4 Representations in the Weak Sense (X XoT), Strong
Sense (X ֊XoT) and the Semi-strong Sense (X a=
XoT). II. The Case of Continuous Local Martingales and
Processes of Bounded Variation......................... 15 2
2. Integral Representations and Change of Time in
Stochastic 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
ix
X
Contents
3. Semimartingales: Basic Notions, Structures, Elements of
Stochastic Analysis 41
3.1 Basic Definitions and Properties ......................... 41
3.2 Canonical Representation. Triplets of Predictable
Characteristics........................................... 52
3.3 Stochastic Integrals with Respect to a Brownian Motion,
Square-integrable Martingales, and Semimartingales ... 56
3.4 Stochastic Differential Equations......................... 73
4. Stochastic Exponential and Stochastic Logarithm.
Cumulant Processes 91
4.1 Stochastic Exponential and Stochastic Logarithm........... 91
4.2 Fourier Cumulant Processes................................ 96
4.3 Laplace Cumulant Processes................................ 99
4.4 Cumulant Processes of Stochastic Integral Transformation
X* = p-X................................................ 101
5. Processes with Independent Increments. Lévy Processes 105
5.1 Processes with Independent Increments and
Semimartingales........................................ 105
5.2 Processes with Stationary Independent Increments (Lévy
Processes)............................................... 108
5.3 Some Properties of Sample Paths of Processes with
Independent Increments................................... 113
5.4 Some Properties of Sample Paths of Processes with
Stationary Independent Increments (Lévy 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 Lévy Processes 135
7.1 Linear and Exponential Levy Models under Change of
Measure.................................................. 135
7.2 On the Criteria of Local Absolute Continuitv of Two
Measures of Lévy Processes............................... 142
Contents xi
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 Lew Processes 151
·./
8.1 Some General Facts about Change of Time for
Semimartingale Models ................................... 151
8.2 Change of Time in Brownian Motion. Different
Formulations............................................. 154
8.3 Change of Time Given by Subordinators. I. Some
Examples................................................. 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
Transaction Costs ....................................... 215
10.4 Asymptotic Arbitrage: Some Problems................... 216 11
11. Change of Measure in Option Pricing 225
хи
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. Lévy Models.......... 254
12. Conditionally Brownian and Lévy Processes. Stochastic
Volatilitv Models 259
С/
12.1 From Black-Scholes Theory of Pricing of Derivatives to
the Implied Volatility. Smile Effect and Stochastic
Volatility Models........................................ 259
12.2 Generalized Inverse Gaussian Subordinator and
Generalized Hyperbolic Lévy Motion: Two Methods of
Construction, Sample Path Properties..................... 270
12.3 Distributional and Sample-path Properties of the Lévy
Processes L(GIG) and L(GH)............................... 275
12.4 On Some Others Models of the Dynamics of Prices.
Comparison of the Properties of Different Models...... 283 13
13. A Wider View. Ambit Processes and Fields, and
Volatility/Intermittency 289
13.1 Introduction............................................. 289
13.2 Ambit Processes and Fields............................... 290
13.3 Lévy Bases and Their Subordination....................... 295
13.4 Change of Lévy Measure................................... 297
13.5 Particular Types of Ambit Processes...................... 300
Afterword 305
Afterword to the Second Edition 307
Bibliography 309
Index
321
|
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| author | Barndorff-Nielsen, Ole E. 1935- Širjaev, Alʹbert N. 1934- |
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| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| indexdate | 2024-07-10T07:08:56Z |
| institution | BVB |
| isbn | 9789814678582 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028188197 |
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| physical | XVIII, 326 S. 24 cm |
| publishDate | 2015 |
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| publisher | World Scientific |
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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 2. ed. Singapore [u.a.] World Scientific 2015 XVIII, 326 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science & applied probability 21 Includes bibliographical references (p. 309-320) and index Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Diskreter stochastischer Prozess (DE-588)4150187-1 gnd rswk-swf Stetigkeit (DE-588)4183167-6 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 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 21 (DE-604)BV011932321 21 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028188197&sequence=000001&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 Stochastischer Prozess (DE-588)4057630-9 gnd Diskreter stochastischer Prozess (DE-588)4150187-1 gnd Stetigkeit (DE-588)4183167-6 gnd Lévy-Prozess (DE-588)4463623-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4150187-1 (DE-588)4183167-6 (DE-588)4463623-4 (DE-588)4079013-7 |
| 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 Stochastischer Prozess (DE-588)4057630-9 gnd Diskreter stochastischer Prozess (DE-588)4150187-1 gnd Stetigkeit (DE-588)4183167-6 gnd Lévy-Prozess (DE-588)4463623-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Stochastic processes Stochastischer Prozess Diskreter stochastischer Prozess Stetigkeit Lévy-Prozess Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028188197&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932321 |
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