Ruin probabilities:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Singapore [u.a.]
World Scientific
2000
|
Schriftenreihe: | Advanced series on statistical science & applied probability
2 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
Beschreibung: | X, 385 S. Illustrationen |
ISBN: | 9810222939 |
Internformat
MARC
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100 | 1 | |a Asmussen, Søren |d 1946- |e Verfasser |0 (DE-588)170289907 |4 aut | |
245 | 1 | 0 | |a Ruin probabilities |c Søren Asmussen |
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336 | |b txt |2 rdacontent | ||
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338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Advanced series on statistical science & applied probability |v 2 | |
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650 | 4 | |a Insurance -- Mathematics | |
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Datensatz im Suchindex
_version_ | 1804127349660188672 |
---|---|
adam_text | Contents
Preface ix
I Introduction 1
1 The risk process 1
2 Claim size distributions 5
3 The arrival process 11
4 A summary of main results and methods 13
5 Conventions 19
II Some general tools and results 23
1 Martingales 24
2 Likelihood ratios and change of measure 26
3 Duality with other applied probability models 30
4 Random walks in discrete or continuous time 33
5 Markov additive processes 39
6 The ladder height distribution 47
III The compound Poisson model 57
1 Introduction 58
2 The Pollaczeck Khinchine formula 61
3 Special cases of the Pollaczeck Khinchine formula 62
4 Change of measure via exponential families 67
5 Lundberg conjugation 69
6 Further topics related to the adjustment coefficient 75
7 Various approximations for the ruin probability 79
8 Comparing the risks of different claim size distributions .... 83
9 Sensitivity estimates 86
10 Estimation of the adjustment coefficient 93
v
vi CONTENTS
IV The probability of ruin within finite time 97
1 Exponential claims 98
2 The ruin probability with no initial reserve 103
3 Laplace transforms 108
4 When does ruin occur? 110
5 Diffusion approximations 117
6 Corrected diffusion approximations 121
7 How does ruin occur? 127
V Renewal arrivals 131
1 Introduction 131
2 Exponential claims. The compound Poisson model with neg¬
ative claims 134
3 Change of measure via exponential families 137
4 The duality with queueing theory 141
VI Risk theory in a Markovian environment 145
1 Model and examples 145
2 The ladder height distribution 152
3 Change of measure via exponential families 160
4 Comparisons with the compound Poisson model 168
5 The Markovian arrival process 173
6 Risk theory in a periodic environment 176
7 Dual queueing models 185
VII Premiums depending on the current reserve 189
1 Introduction 189
2 The model with interest 196
3 The local adjustment coefficient. Logarithmic asymptotics . . 201
VIII Matrix analytic methods 215
1 Definition and basic properties of phase type distributions . . 215
2 Renewal theory 223
3 The compound Poisson model 227
4 The renewal model 229
5 Markov modulated input 234
6 Matrix exponential distributions 240
7 Reserve dependent premiums 244
CONTENTS vii
IX Ruin probabilities in the presence of heavy tails 251
1 Subexponential distributions 251
2 The compound Poisson model 259
3 The renewal model 261
4 Models with dependent input 264
5 Finite horizon ruin probabilities 271
6 Reserve dependent premiums 279
X Simulation methodology 281
1 Generalities 281
2 Simulation via the Pollaczeck Khinchine formula 285
3 Importance sampling via Lundberg conjugation 287
4 Importance sampling for the finite horizon case 290
5 Regenerative simulation 292
6 Sensitivity analysis 294
XI Miscellaneous topics 297
1 The ruin problem for Bernoulli random walk and Brownian
motion. The two barrier ruin problem 297
2 Further applications of martingales 304
3 Large deviations 306
4 The distribution of the aggregate claims 316
5 Principles for premium calculation 323
6 Reinsurance 326
Appendix 331
Al Renewal theory 331
A2 Wiener Hopf factorization 336
A3 Matrix exponentials 340
A4 Some linear algebra 344
A5 Complements on phase type distributions 350
Bibliography 363
Index 383
|
any_adam_object | 1 |
author | Asmussen, Søren 1946- |
author_GND | (DE-588)170289907 |
author_facet | Asmussen, Søren 1946- |
author_role | aut |
author_sort | Asmussen, Søren 1946- |
author_variant | s a sa |
building | Verbundindex |
bvnumber | BV012687242 |
callnumber-first | H - Social Science |
callnumber-label | HG8781 |
callnumber-raw | HG8781.A83 2000 |
callnumber-search | HG8781.A83 2000 |
callnumber-sort | HG 48781 A83 42000 |
callnumber-subject | HG - Finance |
classification_rvk | SK 950 SK 980 SK 820 |
classification_tum | MAT 605f MAT 902f |
ctrlnum | (OCoLC)468132696 (DE-599)BVBBV012687242 |
dewey-full | 368/.01 368/.0121 |
dewey-hundreds | 300 - Social sciences |
dewey-ones | 368 - Insurance |
dewey-raw | 368/.01 368/.01 21 |
dewey-search | 368/.01 368/.01 21 |
dewey-sort | 3368 11 |
dewey-tens | 360 - Social problems and services; associations |
discipline | Mathematik Wirtschaftswissenschaften |
format | Book |
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id | DE-604.BV012687242 |
illustrated | Illustrated |
indexdate | 2024-07-09T18:31:56Z |
institution | BVB |
isbn | 9810222939 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008623655 |
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owner_facet | DE-824 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-384 DE-634 DE-188 DE-83 DE-11 |
physical | X, 385 S. Illustrationen |
publishDate | 2000 |
publishDateSearch | 2000 |
publishDateSort | 2000 |
publisher | World Scientific |
record_format | marc |
series | Advanced series on statistical science & applied probability |
series2 | Advanced series on statistical science & applied probability |
spelling | Asmussen, Søren 1946- Verfasser (DE-588)170289907 aut Ruin probabilities Søren Asmussen Singapore [u.a.] World Scientific 2000 X, 385 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science & applied probability 2 Hier auch später erschienene, unveränderte Nachdrucke Mathematik 501Insurance Mathematics Insurance -- Mathematics Risk Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Versicherungswirtschaft (DE-588)4063206-4 gnd rswk-swf Risikotheorie (DE-588)4135592-1 gnd rswk-swf Finanzwirtschaft (DE-588)4017214-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Finanzwirtschaft (DE-588)4017214-4 s DE-604 Versicherungswirtschaft (DE-588)4063206-4 s Finanzmathematik (DE-588)4017195-4 s Versicherungsmathematik (DE-588)4063194-1 s Risikotheorie (DE-588)4135592-1 s Statistik (DE-588)4056995-0 s 1\p DE-604 Advanced series on statistical science & applied probability 2 (DE-604)BV011932321 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008623655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Asmussen, Søren 1946- Ruin probabilities Advanced series on statistical science & applied probability Mathematik 501Insurance Mathematics Insurance -- Mathematics Risk Finanzmathematik (DE-588)4017195-4 gnd Versicherungswirtschaft (DE-588)4063206-4 gnd Risikotheorie (DE-588)4135592-1 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Statistik (DE-588)4056995-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
subject_GND | (DE-588)4017195-4 (DE-588)4063206-4 (DE-588)4135592-1 (DE-588)4017214-4 (DE-588)4056995-0 (DE-588)4057630-9 (DE-588)4063194-1 |
title | Ruin probabilities |
title_auth | Ruin probabilities |
title_exact_search | Ruin probabilities |
title_full | Ruin probabilities Søren Asmussen |
title_fullStr | Ruin probabilities Søren Asmussen |
title_full_unstemmed | Ruin probabilities Søren Asmussen |
title_short | Ruin probabilities |
title_sort | ruin probabilities |
topic | Mathematik 501Insurance Mathematics Insurance -- Mathematics Risk Finanzmathematik (DE-588)4017195-4 gnd Versicherungswirtschaft (DE-588)4063206-4 gnd Risikotheorie (DE-588)4135592-1 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Statistik (DE-588)4056995-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
topic_facet | Mathematik 501Insurance Mathematics Insurance -- Mathematics Risk Finanzmathematik Versicherungswirtschaft Risikotheorie Finanzwirtschaft Statistik Stochastischer Prozess Versicherungsmathematik |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008623655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV011932321 |
work_keys_str_mv | AT asmussensøren ruinprobabilities |