Stochastic processes: from physics to finance
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2013
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIII, 280 Seiten Diagramme 25 cm |
| ISBN: | 9783319033785 9783319003269 |
Staff View
MARC
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Record in the Search Index
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| DE-BY-FWS_call_number | 2000/SK 820 P324(2) |
| DE-BY-FWS_katkey | 699043 |
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| adam_text | IMAGE 1
CONTENTS
1 A FIRST GLIMPSE OF STOCHASTIC PROCESSES 1
1.1 SOME HISTORY 1
1.2 RANDOM WALK ON A LINE 3
1.2.1 FROM BINOMIAL TO GAUSSIAN 6
1.2.2 FROM BINOMIAL TO POISSON 11
1.2.3 LOG-NORMAL DISTRIBUTION 13
1.3 FURTHER READING 15
2 A BRIEF SURVEY OF THE MATHEMATICS OF PROBABILITY THEORY 17
2.1 SOME BASICS OF PROBABILITY THEORY 17
2.1.1 PROBABILITY SPACES AND RANDOM VARIABLES 18
2.1.2 PROBABILITY THEORY AND LOGIC 21
2.1.3 EQUIVALENT MEASURES 29
2.1.4 DISTRIBUTION FUNCTIONS AND PROBABILITY DENSITIES 30
2.1.5 STATISTICAL INDEPENDENCE AND CONDITIONAL PROBABILITIES ... 31
2.1.6 CENTRAL LIMIT THEOREM 33
2.1.7 EXTREME VALUE DISTRIBUTIONS 35
2.2 STOCHASTIC PROCESSES AND THEIR EVOLUTION EQUATIONS 38
2.2.1 MARTINGALE PROCESSES 41
2.2.2 MARKOV PROCESSES 43
2.3 ITO STOCHASTIC CALCULUS 53
2.3.1 STOCHASTIC INTEGRALS 53
2.3.2 STOCHASTIC DIFFERENTIAL EQUATIONS AND THE ITO FORMULA ... 57 2.4
SUMMARY 58
2.5 FURTHER READING 59
3 DIFFUSION PROCESSES 63
3.1 THE RANDOM WALK REVISITED 63
3.1.1 POLYA PROBLEM 66
3.1.2 RAY LEIGH-PEARSON WALK 69
3.1.3 CONTINUOUS-TIME RANDOM WALK 72
3.2 FREE BROWNIAN MOTION 75
XI
HTTP://D-NB.INFO/1041590679
IMAGE 2
XII CONTENTS
3.2.1 VELOCITY PROCESS 77
3.2.2 POSITION PROCESS 81
3.3 CALDEIRA-LEGGETT MODEL 84
3.3.1 DEFINITION OF THE MODEL 85
3.3.2 VELOCITY PROCESS AND GENERALIZED LANGEVIN EQUATION ... 86 3.4 ON
THE MAXIMAL EXCURSION OF BROWNIAN MOTION 90
3.5 BROWNIAN MOTION IN A POTENTIAL: KRAMERS PROBLEM 92
3.5.1 FIRST PASSAGE TIME FOR ONE-DIMENSIONAL FOKKER-PLANCK EQUATIONS 94
3.5.2 KRAMERS RESULT 97
3.6 A FIRST PASSAGE PROBLEM FOR UNBOUNDED DIFFUSION 98
3.7 KINETIC ISING MODELS AND MONTE CARLO SIMULATIONS 101
3.7.1 PROBABILISTIC STRUCTURE 102
3.7.2 MONTE CARLO KINETICS 102
3.7.3 MEAN-FIELD KINETIC ISING MODEL 105
3.8 QUANTUM MECHANICS AS A DIFFUSION PROCESS 110
3.8.1 HYDRODYNAMICS OF BROWNIAN MOTION 110
3.8.2 CONSERVATIVE DIFFUSION PROCESSES 114
3.8.3 HYPOTHESIS OF UNIVERSAL BROWNIAN MOTION 115
3.8.4 TUNNEL EFFECT 118
3.8.5 HARMONIC OSCILLATOR AND QUANTUM FIELDS 122
3.9 SUMMARY 126
3.10 FURTHER READING 127
4 BEYOND THE CENTRAL LIMIT THEOREM: LEVY DISTRIBUTIONS 131
4.1 BACK TO MATHEMATICS: STABLE DISTRIBUTIONS 132
4.2 THE WEIERSTRASS RANDOM WALK 136
4.2.1 DEFINITION AND SOLUTION 137
4.2.2 SUPERDIFFUSIVE BEHAVIOR 143
4.2.3 GENERALIZATION TO HIGHER DIMENSIONS 147
4.3 FRACTAL-TIME RANDOM WALKS 150
4.3.1 A FRACTAL-TIME POISSON PROCESS 151
4.3.2 SUBDIFFUSIVE BEHAVIOR 154
4.4 A WAY TO AVOID DIVERGING VARIANCE: THE TRUNCATED LEVY FLIGHT . 155
4.5 SUMMARY 159
4.6 FURTHER READING 161
5 MODELING THE FINANCIAL MARKET 163
5.1 BASIC NOTIONS PERTAINING TO FINANCIAL MARKETS 164
5.2 CLASSICAL OPTION PRICING: THE BLACK-SCHOLES THEORY 173
5.2.1 THE BLACK-SCHOLES EQUATION: ASSUMPTIONS AND DERIVATION . 174 5.2.2
THE BLACK-SCHOLES EQUATION: SOLUTION AND INTERPRETATION . 179 5.2.3
RISK-NEUTRAL VALUATION 184
5.2.4 DEVIATIONS FROM BLACK-SCHOLES: IMPLIED VOLATILITY 189 5.3 MODELS
BEYOND GEOMETRIC BROWNIAN MOTION 191
5.3.1 STATISTICAL ANALYSIS OF STOCK PRICES 192
IMAGE 3
CONTENTS XIII
5.3.2 THE VOLATILITY SMILE: PRECURSOR TO GAUSSIAN BEHAVIOR? . . . 205
5.3.3 ARE FINANCIAL TIME SERIES STATIONARY? 209
5.3.4 AGENT BASED MODELING OF FINANCIAL MARKETS 214
5.4 TOWARDS A MODEL OF FINANCIAL CRASHES 221
5.4.1 SOME EMPIRICAL PROPERTIES 222
5.4.2 A MARKET MODEL: FROM SELF-ORGANIZATION TO CRITICALITY . . . 225
5.5 SUMMARY 233
5.6 FURTHER READING 234
APPENDIX A STABLE DISTRIBUTIONS REVISITED 237
A. 1 TESTING FOR DOMAINS OF ATTRACTION 237
A.2 CLOSED-FORM EXPRESSIONS AND ASYMPTOTIC BEHAVIOR 239
APPENDIX B HYPERSPHERICAL POLAR COORDINATES 243
APPENDIX C THE WEIERSTRASS RANDOM WALK REVISITED 247
APPENDIX D THE EXPONENTIALLY TRUNCATED LEVY FLIGHT 253
APPENDIX E PUT-CALL PARITY 259
APPENDIX F GEOMETRIC BROWNIAN MOTION 261
REFERENCES 265
INDEX 273
|
| any_adam_object | 1 |
| author | Paul, Wolfgang 1959- Baschnagel, Jörg 1965- |
| author_GND | (DE-588)121472302 (DE-588)121472329 |
| author_facet | Paul, Wolfgang 1959- Baschnagel, Jörg 1965- |
| author_role | aut aut |
| author_sort | Paul, Wolfgang 1959- |
| author_variant | w p wp j b jb |
| building | Verbundindex |
| bvnumber | BV041297975 |
| classification_rvk | SK 820 UG 3900 |
| ctrlnum | (OCoLC)858033687 (DE-599)DNB1041590679 |
| dewey-full | 519.23 |
| 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 | Physik Mathematik Wirtschaftswissenschaften |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV041297975 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-20T07:16:33Z |
| institution | BVB |
| isbn | 9783319033785 9783319003269 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026746824 |
| oclc_num | 858033687 |
| open_access_boolean | |
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| owner_facet | DE-19 DE-BY-UBM DE-29T DE-83 DE-473 DE-BY-UBG DE-20 DE-862 DE-BY-FWS DE-188 |
| physical | XIII, 280 Seiten Diagramme 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Paul, Wolfgang 1959- Baschnagel, Jörg 1965- Stochastic processes from physics to finance Finanzmathematik (DE-588)4017195-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4057630-9 (DE-588)4037952-8 |
| title | Stochastic processes from physics to finance |
| title_auth | Stochastic processes from physics to finance |
| title_exact_search | Stochastic processes from physics to finance |
| title_full | Stochastic processes from physics to finance Wolfgang Paul ; Jörg Baschnagel |
| title_fullStr | Stochastic processes from physics to finance Wolfgang Paul ; Jörg Baschnagel |
| title_full_unstemmed | Stochastic processes from physics to finance Wolfgang Paul ; Jörg Baschnagel |
| title_short | Stochastic processes |
| title_sort | stochastic processes from physics to finance |
| title_sub | from physics to finance |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Finanzmathematik Stochastischer Prozess Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026746824&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT paulwolfgang stochasticprocessesfromphysicstofinance AT baschnageljorg stochasticprocessesfromphysicstofinance |
Indexes
Sonderstandort Fakultät
| Call Number: |
2000 SK 820 P324(2) |
|---|---|
| Copy 1 | nicht ausleihbar Checked out – Due: 31.12.2099 Recall This |