Sparse grid quadrature in high dimensions with applications in finance and insurance:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Lecture Notes in Computational Science and Engineering
77 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | VIII, 182 S. Ill., graph. Darst. |
| ISBN: | 9783642160042 9783642160035 |
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MARC
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Record in the Search Index
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IMAGE 1
CONTENTS
1 INTRODUCTION 1
2 DIMENSION-WISE DECOMPOSITIONS 11
2.1 CLASSICAL ANOVA DECOMPOSITION 13
2.1.1 EFFECTIVE DIMENSIONS 16
2.1.2 ERROR BOUNDS 19
2.2 ANCHORED-ANOVA DECOMPOSITION 21
2.2.1 EFFECTIVE DIMENSIONS 22
2.2.2 ERROR BOUNDS 26
3 DIMENSION-WISE QUADRATURE 29
3.1 CLASSICAL MULTIVARIATE QUADRATURE METHODS 29
3.1.1 MONTE CARLO 31
3.1.2 QUASI-MONTE CARLO 34
3.1.3 PRODUCT METHODS 38
3.2 DIMENSION-WISE QUADRATURE METHODS 43
3.2.1 TRUNCATION AND DISCRETIZATION 43
3.2.2 ERROR AND COSTS 45
3.2.3 A PRIORI CONSTRUCTION 47
3.2.4 DIMENSION-ADAPTIVE CONSTRUCTION 49
4 SPARSE GRID QUADRATURE 51
4.1 SPARSE GRID METHODS 51
4.1.1 CLASSICAL CONSTRUCTION 52
4.1.2 DELAYED BASIS SEQUENCES 55
4.1.3 GENERALISED SPARSE GRIDS 59
4.1.4 DIMENSION-ADAPTIVE SPARSE GRIDS 61
4.2 OPTIMAL SPARSE GRIDS IN WEIGHTED SPACES 63
4.2.1 COST-BENEFIT RATIO 64
4.2.2 COST ANALYSIS 67
4.2.3 ERROR ANALYSIS 69
HTTP://D-NB.INFO/100650818X
IMAGE 2
VIII C O N T E N T S
4.2.4 ANALYSIS OF ERROR VERSUS COST 71
4.3 RELATION TO DIMENSION-WISE QUADRATURE 74
5 DIMENSION REDUCTION AND SMOOTHING 77
5.1 DIMENSION REDUCTION 77
5.1.1 RANDOM WALK, BROWNIAN BRIDGE, PCA 78
5.1.2 LINEAR TRANSFORMATIONS 82
5.2 DOMAIN DECOMPOSITION 89
5.2.1 ROOT FINDING 89
5.2.2 HYPERPLANE ARRANGEMENTS 90
5.2.3 CONDITIONAL SAMPLING 98
6 VALIDATION AND APPLICATIONS 101
6.1 INTEREST RATES DERIVATIVES 104
6.1.1 ZERO COUPON BONDS 104
6.1.2 COLLATERALIZED MORTGAGE OBLIGATIONS 109
6.2 PATH-DEPENDENT OPTIONS 114
6.2.1 ASIAN OPTIONS 115
6.2.2 BARRIER OPTIONS 120
6.3 PERFORMANCE-DEPENDENT OPTIONS 125
6.3.1 FRAMEWORK AND PRICING FORMULAS 125
6.3.2 NUMERICAL RESULTS 131
6.4 ASSET-LIABILITY MANAGEMENT IN LIFE INSURANCE 136
6.4.1 MODEL AND INTEGRAL REPRESENTATION 136
6.4.2 NUMERICAL RESULTS 145
6.5 SUMMARY AND DISCUSSION 149
7 SUMMARY AND CONCLUSIONS 153
A DISCREPANCY AND TRACTABILITY 157
A.L REPRODUCING KERNEL HILBERT SPACES 157
A.2 NOTIONS OF DISCREPANCY 161
A.3 TRACTABILITY RESULTS 167
REFERENCES 172
INDEX 179 |
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| author | Holtz, Markus |
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| dewey-tens | 330 - Economics 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-20T10:52:42Z |
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| isbn | 9783642160042 9783642160035 |
| language | English |
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| physical | VIII, 182 S. Ill., graph. Darst. |
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| series | Lecture Notes in Computational Science and Engineering |
| series2 | Lecture Notes in Computational Science and Engineering |
| spelling | Holtz, Markus Verfasser aut Sparse grid quadrature in high dimensions with applications in finance and insurance Markus Holtz Berlin [u.a.] Springer 2011 VIII, 182 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Computational Science and Engineering 77 Dünnes Gitter (DE-588)4411841-7 gnd rswk-swf Numerische Integration (DE-588)4172168-8 gnd rswk-swf Numerische Integration (DE-588)4172168-8 s Dünnes Gitter (DE-588)4411841-7 s DE-604 Lecture Notes in Computational Science and Engineering 77 (DE-604)BV011386476 77 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3532059&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020716060&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holtz, Markus Sparse grid quadrature in high dimensions with applications in finance and insurance Lecture Notes in Computational Science and Engineering Dünnes Gitter (DE-588)4411841-7 gnd Numerische Integration (DE-588)4172168-8 gnd |
| subject_GND | (DE-588)4411841-7 (DE-588)4172168-8 |
| title | Sparse grid quadrature in high dimensions with applications in finance and insurance |
| title_auth | Sparse grid quadrature in high dimensions with applications in finance and insurance |
| title_exact_search | Sparse grid quadrature in high dimensions with applications in finance and insurance |
| title_full | Sparse grid quadrature in high dimensions with applications in finance and insurance Markus Holtz |
| title_fullStr | Sparse grid quadrature in high dimensions with applications in finance and insurance Markus Holtz |
| title_full_unstemmed | Sparse grid quadrature in high dimensions with applications in finance and insurance Markus Holtz |
| title_short | Sparse grid quadrature in high dimensions with applications in finance and insurance |
| title_sort | sparse grid quadrature in high dimensions with applications in finance and insurance |
| topic | Dünnes Gitter (DE-588)4411841-7 gnd Numerische Integration (DE-588)4172168-8 gnd |
| topic_facet | Dünnes Gitter Numerische Integration |
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