Monte Carlo and quasi-Monte-Carlo sampling:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schriftenreihe: | Springer series in statistics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018658648&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 373 S. graph. Darst. |
| ISBN: | 9780387781648 |
Internformat
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| 100 | 1 | |a Lemieux, Christiane |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Monte Carlo and quasi-Monte-Carlo sampling |c Christiane Lemieux |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 629f 2012 A 3062 |
|---|---|
| DE-BY-TUM_katkey | 1845110 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071406585 |
| _version_ | 1821933753813958657 |
| adam_text | Titel: Monte Carlo and Quasi-Monte Carlo sampling
Autor: Lemieux, Christiane
Jahr: 2009
Contents
The Monte Carlo Method ................................ 1
1.1 Monte Carlo method for integration ...................... 3
1.2 Connection with stochastic simulation..................... 12
1.3 Alternative formulation of the integration problem via /:
an example............................................ 20
1.4 A primer on uniform random number generation........... 22
1.5 Using Monte Carlo to approximate a distribution........... 25
1.6 Two more examples..................................... 27
Problems .................................................. 34
Sampling from Known Distributions...................... 41
2.1 Common distributions arising in stochastic models.......... 42
2.2 Inversion.............................................. 44
2.3 Acceptance-rejection.................................... 46
2.4 Composition........................................... 48
2.5 Convolution and other useful identities.................... 50
2.6 Multivariate case....................................... 51
Problems.................................................. 55
Pseudorandom Number Generators....................... 57
3.1 Basic concepts and definitions............................ 58
3.2 Generators based on linear recurrences.................... 60
3.2.1 Recurrences over Z,n for m 2 .................... 61
3.2.2 Recurrences modulo 2............................. 64
3.3 Add-with-carry and subtract-with-borrow generators........ 66
3.4 Nonlinear generators.................................... 67
3.5 Theoretical and statistical testing......................... 68
3.5.1 Theoretical tests for MRGs........................ 70
3.5.2 Theoretical tests for PRNGs based on recurrences
modulo 2........................................ 75
3.5.3 Statistical tests .................................. 80
Contents
Problems .................................................. 85
Variance Reduction Techniques........................... 87
4.1 Introduction........................................... 87
4.2 Efficiency.............................................. 89
4.3 Antithetic variates...................................... 89
4.4 Control variates........................................101
4.5 Importance sampling....................................Ill
4.6 Conditional .Monte Carlo................................119
4.7 Stratification...........................................125
4.8 Common random numbers...............................132
4.9 Combinations of techniques..............................135
Problems ..................................................136
Quasi-Monte Carlo Constructions........................ 139
5.1 Introduction........................................... 139
5.2 Main constructions: basic principles....................... 143
5.3 Lattices............................................... 146
5.4 Digital nets and sequences............................... 153
5.4.1 Sobol sequence.................................. 157
5.4.2 Faure sequence................................... 161
5.4.3 Niederreiter sequences ............................ 163
5.4.4 Improvements to the original constructions
of Halton, Sobol . Niederreiter. and Faure ........... 164
5.4.5 Digital net constructions and extensions............. 170
5.5 Recurrence-based point sets.............................. 174
5.6 Quality measures....................................... 179
5.6.1 Discrepancy and related measures..................180
5.6.2 Criteria based on Fourier and
Walsh decompositions.............................187
5.6.3 Motivation for going beyond error bounds...........197
Problems ..................................................197
Using Quasi—Monte Carlo in Practice.....................201
6.1 Introduction...........................................201
6.2 Randomized quasi -Monte Carlo..........................202
6.2.1 Random shift (or rotation sampling)................204
6.2.2 Digital shift .....................................206
6.2.3 Scrambling and permutations......................206
6.2.4 Partitions and Latin supercube sampling............209
6.2.5 Array-RQMC....................................210
6.2.6 Studying the variance.............................211
6.3 AN OVA decomposition and effective dimension ............214
6.3.1 Effective dimension...............................216
6.3.2 Brownian bridge and related techniques.............222
Contents xiii
6.3.3 Methods for estimating a]
and approximating fj(u)..........................225
6.3.4 Using the ANOVA insight to find
good constructions ...............................228
6.4 Using quasi- Monte Carlo sampling for simulation...........229
6.5 Suggestions for practitioners.............................237
Problems ..................................................239
Appendix: Tractability, weighted spaces
and component-by-component constructions...............241
7 Financial Applications....................................247
7.1 European option pricing under the lognormal model........247
7.2 More complex models...................................256
7.2.1 Heston s process..................................257
7.2.2 Regime switching model...........................258
7.2.3 Variance gamma model ...........................260
7.3 Randomized quasi Monte Carlo methods in finance.........260
7.4 Commonly used variance reduction techniques .............273
7.4.1 Antithetic variates................................ 273
7.4.2 Control variates.................................. 273
7.4.3 Importance sampling............................. 275
7.4.4 Conditional Monte Carlo.......................... 279
7.4.5 Common random numbers......................... 281
7.4.6 Moment-matching methods........................ 282
7.5 American option pricing................................. 283
7.6 Estimating sensitivities and percentiles.................... 288
Problems .................................................. 298
8 Beyond Numerical Integration............................301
8.1 Markov Chain Monte Carlo (MCMC).....................303
8.1.1 Metropolis-Hastings algorithm.....................305
8.1.2 Exact sampling ..................................310
8.2 Sequential Monte Carlo.................................312
8.3 Computer experiments..................................320
Problems ..................................................332
A Review of Algebra........................................335
B Error and Variance Analysis for Halton Sequences........341
References....................................................347
Index.........................................................369
|
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| id | DE-604.BV035799488 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:00:28Z |
| institution | BVB |
| isbn | 9780387781648 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018658648 |
| oclc_num | 610986744 |
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| owner_facet | DE-473 DE-BY-UBG DE-739 DE-11 DE-703 DE-91G DE-BY-TUM |
| physical | XVI, 373 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spellingShingle | Lemieux, Christiane Monte Carlo and quasi-Monte-Carlo sampling Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4240945-7 |
| title | Monte Carlo and quasi-Monte-Carlo sampling |
| title_auth | Monte Carlo and quasi-Monte-Carlo sampling |
| title_exact_search | Monte Carlo and quasi-Monte-Carlo sampling |
| title_full | Monte Carlo and quasi-Monte-Carlo sampling Christiane Lemieux |
| title_fullStr | Monte Carlo and quasi-Monte-Carlo sampling Christiane Lemieux |
| title_full_unstemmed | Monte Carlo and quasi-Monte-Carlo sampling Christiane Lemieux |
| title_short | Monte Carlo and quasi-Monte-Carlo sampling |
| title_sort | monte carlo and quasi monte carlo sampling |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018658648&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lemieuxchristiane montecarloandquasimontecarlosampling |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 629f 2012 A 3062 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |