Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton u.a.
Chapman & Hall
2001
|
| Schriftenreihe: | Applied mathematics and mathematical computation
17 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009712909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 319 S. |
Internformat
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| 100 | 1 | |a Meyer, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Continuous stochastic calculus with applications to finance |c Michael Meyer |
| 264 | 1 | |a Boca Raton u.a. |b Chapman & Hall |c 2001 | |
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| 490 | 1 | |a Applied mathematics and mathematical computation |v 17 | |
| 650 | 4 | |a Analyse stochastique | |
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| 650 | 4 | |a Finances - Modèles mathématiques | |
| 650 | 7 | |a Finances - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Financiering |2 gtt | |
| 650 | 7 | |a Martingalen |2 gtt | |
| 650 | 7 | |a Stochastische analyse |2 gtt | |
| 650 | 7 | |a Stochastische integratie |2 gtt | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Stochastic analysis | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 606f 2001 A 25035 |
|---|---|
| DE-BY-TUM_katkey | 1256317 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020278048 |
| _version_ | 1821932663279190016 |
| adam_text | Table of Contents ix
TABLE OF CONTENTS
Chapter I Martingale Theory
Preliminaries
1. Convergence of Random Variables 2
1. a Forms of convergence 2
l.b Norm convergence and uniform integrability 3
2. Conditioning 8
2.a Sigma fields, information and conditional expectation 8
2.b Conditional expectation 10
3. Submartingales 19
3.a Adapted stochastic processes 19
3.b Sampling at optional times 22
3.c Application to the gambler s ruin problem 25
4. Convergence Theorems 29
4.a Upcrossings 29
4.b Reversed submartingales 34
4.c Levi s Theorem 36
4.d Strong Law of Large Numbers 38
5. Optional Sampling of Closed Submartingale Sequences 42
5.a Uniform integrability, last elements, closure 42
5.b Sampling of closed submartingale sequences 44
6. Maximal Inequalities for Submartingale Sequences 47
6.a Expectations as Lebesgue integrals 47
6.b Maximal inequalities for submartingale sequences 47
7. Continuous Time Martingales 50
7.a Filtration, optional times, sampling 50
7.b Pathwise continuity 56
7.c Convergence theorems 59
7.d Optional sampling theorem 62
7.e Continuous time £p inequalities 64
8. Local Martingales 65
8.a Localization 65
8.b Bayes Theorem 71
x Table of Contents
9. Quadratic Variation 73
9.a Square integrable martingales 73
9.b Quadratic variation 74 .
9.c Quadratic variation and L2 bounded martingales 86
9.d Quadratic variation and i1 bounded martingales 88
10. The Covariation Process 90
10.a Definition and elementary properties 90
10.b Integration with respect to continuous bounded variation processes . 91
10.c Kunita Watanabe inequality 94
11. Semimartingales 98
11.a Definition and basic properties 98
11.b Quadratic variation and covariation 99
Chapter II Brownian Motion
1. Gaussian Processes 103
l.a Gaussian random variables in Rk 103
l.b Gaussian processes 109
l.c Isonormal processes Ill
2. One Dimensional Brownian Motion 112
2.a One dimensional Brownian motion starting at zero 112
2.b Pathspace and Wiener measure 116
2.c The measures Px 118
2.d Brownian motion in higher dimensions 118
2.e Markov property 120
2.f The augmented filtration (Tt) 127
2.g Miscellaneous properties 128
Chapter III Stochastic Integration
1. Measurability Properties of Stochastic Processes 131
l.a The progressive and predictable r fields on II 131
l.b Stochastic intervals and the optional a field 134
2. Stochastic Integration with Respect to Continuous Semimartingales . . 135
2.a Integration with respect to continuous local martingales 135
2.b M integrable processes 140
2.c Properties of stochastic integrals with respect to continuous
local martingales 142
2.d Integration with respect to continuous semimartingales 147
2.e The stochastic integral as a limit of certain Riemann type sums . . 150
2.f Integration with respect to vector valued continuous semimartingales 153
Table of Contents xi
3. Ito s Formula 157
3.a Ito s formula 157
3.b Differential notation 160
3.c Consequences of Ito s formula 161
3.d Stock prices 165
3.e Levi s characterization of Brownian motion 166
3.f The multiplicative compensator Ux 168
3.g Harmonic functions of Brownian motion 169
4. Change of Measure 170
4.a Locally equivalent change of probability 170
4.b The exponential local martingale 173
4.c Girsanov s theorem 175
4.d The Novikov condition 180
5. Representation of Continuous Local Martingales 183
5.a Time change for continuous local martingales 183
5.b Brownian functionals as stochastic integrals 187
5.c Integral representation of square integrable Brownian martingales . 192
5.d Integral representation of Brownian local martingales 195
5.e Representation of positive Brownian martingales 196
5.f Kunita Watanabe decomposition 196
6. Miscellaneous 200
6.a Ito processes 200
6.b Volatilities 203
6.c Call option lemmas 205
6.d Log Gaussian processes 208
6.e Processes with finite time horizon 209
Chapter IV Application to Finance
1. The Simple Black Scholes Market 211
l.a The model 211
l.b Equivalent martingale measure 212
l.c Trading strategies and absence of arbitrage 213
2. Pricing of Contingent Claims 218
2.a Replication of contingent claims 218
2.b Derivatives of the form h = f{Sr) 221
2.c Derivatives of securities paying dividends 225
3. The General Market Model 228
3.a Preliminaries 228
3.b Markets and trading strategies 229
xii Table of Contents
3.c Deflators 232
3.d Numeraires and associated equivalent probabilities 235
3.e Absence of arbitrage and existence of a local spot
martingale measure 238
3.f Zero coupon bonds and interest rates 243
3.g General Black Scholes model and market price of risk 246
4. Pricing of Random Payoffs at Fixed Future Dates 251
4.a European options 251
4.b Forward contracts and forward prices 254
4.c Option to exchange assets 254
4.d Valuation of non path dependent options in Gaussian models . . . 259
4.e Delta hedging 265
4.f Connection with partial differential equations 267
5. Interest Rate Derivatives 276
5.a Floating and fixed rate bonds 276
5.b Interest rate swaps 277
5.c Swaptions 278
5.d Interest rate caps and floors 280
5.e Dynamics of the Libor process 281
5.f Libor models with prescribed volatilities 282
5.g Cap valuation in the log Gaussian Libor model 285
5.h Dynamics of forward swap rates 286
5.i Swap rate models with prescribed volatilities 288
5.j Valuation of swaptions in the log Gaussian swap rate model .... 291
5.k Replication of claims 292
Appendix
A. Separation of convex sets 297
B. The basic extension procedure 299
C. Positive semidefinite matrices 305
D. Kolmogoroff existence theorem 306
|
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| id | DE-604.BV014169084 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:00:35Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009712909 |
| oclc_num | 44927108 |
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| physical | XVI, 319 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Applied mathematics and mathematical computation |
| series2 | Applied mathematics and mathematical computation |
| spellingShingle | Meyer, Michael Continuous stochastic calculus with applications to finance Applied mathematics and mathematical computation Analyse stochastique Analyse stochastique ram Finances - Modèles mathématiques Finances - Modèles mathématiques ram Financiering gtt Martingalen gtt Stochastische analyse gtt Stochastische integratie gtt Wiskundige modellen gtt Mathematisches Modell Finance Mathematical models Stochastic analysis Stochastik (DE-588)4121729-9 gnd Finanzmathematik (DE-588)4017195-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4017195-4 (DE-588)4064324-4 |
| title | Continuous stochastic calculus with applications to finance |
| title_auth | Continuous stochastic calculus with applications to finance |
| title_exact_search | Continuous stochastic calculus with applications to finance |
| title_full | Continuous stochastic calculus with applications to finance Michael Meyer |
| title_fullStr | Continuous stochastic calculus with applications to finance Michael Meyer |
| title_full_unstemmed | Continuous stochastic calculus with applications to finance Michael Meyer |
| title_short | Continuous stochastic calculus with applications to finance |
| title_sort | continuous stochastic calculus with applications to finance |
| topic | Analyse stochastique Analyse stochastique ram Finances - Modèles mathématiques Finances - Modèles mathématiques ram Financiering gtt Martingalen gtt Stochastische analyse gtt Stochastische integratie gtt Wiskundige modellen gtt Mathematisches Modell Finance Mathematical models Stochastic analysis Stochastik (DE-588)4121729-9 gnd Finanzmathematik (DE-588)4017195-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Analyse stochastique Finances - Modèles mathématiques Financiering Martingalen Stochastische analyse Stochastische integratie Wiskundige modellen Mathematisches Modell Finance Mathematical models Stochastic analysis Stochastik Finanzmathematik Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009712909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV006188231 |
| work_keys_str_mv | AT meyermichael continuousstochasticcalculuswithapplicationstofinance |
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Teilbibliothek Mathematik & Informatik
| Signatur: | 0102 MAT 606f 2001 A 25035 |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |