Modern actuarial risk theory:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer Acad. Publ.
2002
|
| Ausgabe: | Reprint. with minor corr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. 291 - 295 |
| Beschreibung: | XVIII, 306 S. graph. Darst. |
| ISBN: | 1402029527 9781402029523 |
Internformat
MARC
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| 245 | 1 | 0 | |a Modern actuarial risk theory |c by Rob Kaas ... |
| 250 | |a Reprint. with minor corr. | ||
| 264 | 1 | |a Boston [u.a.] |b Kluwer Acad. Publ. |c 2002 | |
| 300 | |a XVIII, 306 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 291 - 295 | ||
| 650 | 4 | |a Risiko - Versicherungsmathematik | |
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Datensatz im Suchindex
| _version_ | 1804137514401792000 |
|---|---|
| adam_text | Contents
Foreword
Preface
I Utility theory and insurance
1.1
Introduction
1.2
The expected utility model
1.3
Classes of utility
f
unctions
1.4
Optimality of stop-loss reinsurance
1.5
Exercises
2
The
,
individual risk model
2.1
Introduction
2.2
Mixed distributions and risks
2.3
Convolution
2.4
Transforms
2.5
Approximations
V
vii
1
1
2
7
10
15
19
19
20
28
31
34
xv
xvi CONTENTS
2.6
Application: optimal reinsurance
39
2.7
Exercises
40
3
Collective
risk models
45
3.1
Introduction
45
3.2
Compound distributions
46
3.3
Distributions for the number of claims
50
3.4
Compound
Poisson
distributions
52
3.5
Panjer s recursion
54
3.6
Approximations for compound distributions
59
3.7
Individual and collective risk model
60
3.8
Some parametric claim size distributions
63
3.9
Stop-loss insurance and approximations
67
3.10
Stop-loss premiums in case of unequal variances
71
3.1
1 Exercises
75
4
Ruin theory
81
4.1
Introduction
81
4.2
The risk process
83
4.3
Exponential upper bound
85
4.4
Ruin probability and exponential claims
88
4.5
Discrete time model
91
4.6
Reinsurance and ruin probabilities
92
4.7
Beekman s
convolution formula
95
4.8
Explicit expressions for ruin probabilities
100
4.9
Approximation of ruin probabilities
103
4.10
Exercises
105
5
Premium principles
109
5.1
Introduction
109
5.2
Premium calculation from top-down
110
5.3
Various premium principles
113
5.4
Properties of premium principles
115
CONTENTS xvii
5.5
Characterizations
oj
premium principles
118
5.6
Premium reduction by coinsurance
121
5.7
Exercises
122
6
Bonus-malus systems
125
6.1
Introduction
125
6.2
An example of a bonus-malus system
126
6.3
Markov analysis
129
6.4
Exercises
135
7
Credibility theory
137
7. /
Introduction
137
7.2
The balanced
Bühlmann
model
139
7.3
More general credibility models
147
7.4
The
Bühlmann-Straub
model
151
7.5
Negative binomial model for the number of car insurance
claims
158
7.6
Exercises
164
8
Generalized linear models
167
8.1
Introduction
167
8.2
Generalized Linear Models
169
8.3
Some traditional estimation procedures and GLM s
172
8.4
Deviance and scaled deviance
180
8.5
Example: analysis of a contingency table
184
8.6
The stochastic component of GLM s
188
8.7
Exercises
198
9
IBNR techniques
201
9.1
Introduction
201
9.2
A GLM that encompasses various IBNR methods
205
9.3
Illustration of some IBNR methods
211
9.4
Exercises
218
xviii CONTENTS
10
Ordering
ofrisks
221
10.1
Introduction
221
10.2
Larger
risks
224
10.3
More dangerous risks
227
10.4
Applications
234
10.5
Incomplete information
243
10.6
Sums of dependent random variables
250
10.7
Exercises
263
Hints for the exercises
271
Notes and references
287
Tables
298
Index
300
MODERN
ACTUARIAL RISK THEORY
Rob
Kaas,
Marc
Goovaerts,
Jan Dhaene and Michel Denuit
Apart from standard actuarial theory, Modern Actuarial Risk Theory contains methods
that are relevant for actuarial practice, for instance the rating of automobile insurance
policies, premium principles and IBNR models, as well as generalized linear models
with an eye on actuarial applications. Furthermore extensive introductions are given
to credibility theory and ordering of risks. The book reflects the state of the art in
actuarial risk theory. In addition to some chapters which are compatible with official
material of actuarial education in North-America, Europe and other parts of the world,
the book contains important material on topics that are relevant for recent insurance
and actuarial developments including determining solvency measures, fair-value
computations, reserving, ranking of risks, modelling dependencies and the use of
generalized linear models. Basic ideas on risk measures in the framework of
insurance premiums are also considered. The numerous exercises contained in
Modern Actuarial Risk Theory, together with the hints for solving the more difficult
ones and the numerical answers to many others, make the book useful as a textbook.
Some important practical paradigms in insurance are presented in a way that is
appealing to actuaries in their daily business. The mathematical background
assumed is on a level such as acquired in the first stage of a bachelors program in
quantitative economics or mathematical statistics.
Rob
Kaas
is a professor of
actuariat
statistics at the University of Amsterdam and the
Catholic University of
Leuven.
Marc Goovaerts and Jan Dhaene are professors of
non-life
actuariat
science at these same universities, while Michel Denuit holds a
similar position at the
Université Catholique de
Louvain. Marc Goovaerts and Rob
Kaas
published books on various topics in non-life actuarial science, including
Credibility Theory. IBNR-methods and Ordering of Risks.
|
| adam_txt |
Contents
Foreword
Preface
I Utility theory and insurance
1.1
Introduction
1.2
The expected utility model
1.3
Classes of utility
f
unctions
1.4
Optimality of stop-loss reinsurance
1.5
Exercises
2
The
,
individual risk model
2.1
Introduction
2.2
Mixed distributions and risks
2.3
Convolution
2.4
Transforms
2.5
Approximations
V
vii
1
1
2
7
10
15
19
19
20
28
31
34
xv
xvi CONTENTS
2.6
Application: optimal reinsurance
39
2.7
Exercises
40
3
Collective
risk models
45
3.1
Introduction
45
3.2
Compound distributions
46
3.3
Distributions for the number of claims
50
3.4
Compound
Poisson
distributions
52
3.5
Panjer's recursion
54
3.6
Approximations for compound distributions
59
3.7
Individual and collective risk model
60
3.8
Some parametric claim size distributions
63
3.9
Stop-loss insurance and approximations
67
3.10
Stop-loss premiums in case of unequal variances
71
3.1
1 Exercises
75
4
Ruin theory
81
4.1
Introduction
81
4.2
The risk process
83
4.3
Exponential upper bound
85
4.4
Ruin probability and exponential claims
88
4.5
Discrete time model
91
4.6
Reinsurance and ruin probabilities
92
4.7
Beekman's
convolution formula
95
4.8
Explicit expressions for ruin probabilities
100
4.9
Approximation of ruin probabilities
103
4.10
Exercises
105
5
Premium principles
109
5.1
Introduction
109
5.2
Premium calculation from top-down
110
5.3
Various premium principles
113
5.4
Properties of premium principles
115
CONTENTS xvii
5.5
Characterizations
oj
premium principles
118
5.6
Premium reduction by coinsurance
121
5.7
Exercises
122
6
Bonus-malus systems
125
6.1
Introduction
125
6.2
An example of a bonus-malus system
126
6.3
Markov analysis
129
6.4
Exercises
135
7
Credibility theory
137
7. /
Introduction
137
7.2
The balanced
Bühlmann
model
139
7.3
More general credibility models
147
7.4
The
Bühlmann-Straub
model
151
7.5
Negative binomial model for the number of car insurance
claims
158
7.6
Exercises
164
8
Generalized linear models
167
8.1
Introduction
167
8.2
Generalized Linear Models
169
8.3
Some traditional estimation procedures and GLM's
172
8.4
Deviance and scaled deviance
180
8.5
Example: analysis of a contingency table
184
8.6
The stochastic component of GLM's
188
8.7
Exercises
198
9
IBNR techniques
201
9.1
Introduction
201
9.2
A GLM that encompasses various IBNR methods
205
9.3
Illustration of some IBNR methods
211
9.4
Exercises
218
xviii CONTENTS
10
Ordering
ofrisks
221
10.1
Introduction
221
10.2
Larger
risks
224
10.3
More dangerous risks
227
10.4
Applications
234
10.5
Incomplete information
243
10.6
Sums of dependent random variables
250
10.7
Exercises
263
Hints for the exercises
271
Notes and references
287
Tables
298
Index
300
MODERN
ACTUARIAL RISK THEORY
Rob
Kaas,
Marc
Goovaerts,
Jan Dhaene and Michel Denuit
Apart from standard actuarial theory, Modern Actuarial Risk Theory contains methods
that are relevant for actuarial practice, for instance the rating of automobile insurance
policies, premium principles and IBNR models, as well as generalized linear models
with an eye on actuarial applications. Furthermore extensive introductions are given
to credibility theory and ordering of risks. The book reflects the state of the art in
actuarial risk theory. In addition to some chapters which are compatible with official
material of actuarial education in North-America, Europe and other parts of the world,
the book contains important material on topics that are relevant for recent insurance
and actuarial developments including determining solvency measures, fair-value
computations, reserving, ranking of risks, modelling dependencies and the use of
generalized linear models. Basic ideas on risk measures in the framework of
insurance premiums are also considered. The numerous exercises contained in
Modern Actuarial Risk Theory, together with the hints for solving the more difficult
ones and the numerical answers to many others, make the book useful as a textbook.
Some important practical paradigms in insurance are presented in a way that is
appealing to actuaries in their daily business. The mathematical background
assumed is on a level such as acquired in the first stage of a bachelors program in
quantitative economics or mathematical statistics.
Rob
Kaas
is a professor of
actuariat
statistics at the University of Amsterdam and the
Catholic University of
Leuven.
Marc Goovaerts and Jan Dhaene are professors of
non-life
actuariat
science at these same universities, while Michel Denuit holds a
similar position at the
Université Catholique de
Louvain. Marc Goovaerts and Rob
Kaas
published books on various topics in non-life actuarial science, including
Credibility Theory. IBNR-methods and Ordering of Risks. |
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| id | DE-604.BV023224943 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:17:35Z |
| indexdate | 2024-07-09T21:13:30Z |
| institution | BVB |
| isbn | 1402029527 9781402029523 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016410782 |
| oclc_num | 255365070 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XVIII, 306 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| spelling | Modern actuarial risk theory by Rob Kaas ... Reprint. with minor corr. Boston [u.a.] Kluwer Acad. Publ. 2002 XVIII, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 291 - 295 Risiko - Versicherungsmathematik Versicherungswirtschaft (DE-588)4063206-4 gnd rswk-swf Risikotheorie (DE-588)4135592-1 gnd rswk-swf Risikotheorie (DE-588)4135592-1 s Versicherungswirtschaft (DE-588)4063206-4 s DE-604 Kaas, Rob Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016410782&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016410782&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Modern actuarial risk theory Risiko - Versicherungsmathematik Versicherungswirtschaft (DE-588)4063206-4 gnd Risikotheorie (DE-588)4135592-1 gnd |
| subject_GND | (DE-588)4063206-4 (DE-588)4135592-1 |
| title | Modern actuarial risk theory |
| title_auth | Modern actuarial risk theory |
| title_exact_search | Modern actuarial risk theory |
| title_exact_search_txtP | Modern actuarial risk theory |
| title_full | Modern actuarial risk theory by Rob Kaas ... |
| title_fullStr | Modern actuarial risk theory by Rob Kaas ... |
| title_full_unstemmed | Modern actuarial risk theory by Rob Kaas ... |
| title_short | Modern actuarial risk theory |
| title_sort | modern actuarial risk theory |
| topic | Risiko - Versicherungsmathematik Versicherungswirtschaft (DE-588)4063206-4 gnd Risikotheorie (DE-588)4135592-1 gnd |
| topic_facet | Risiko - Versicherungsmathematik Versicherungswirtschaft Risikotheorie |
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