Generalized Poisson models and their applications in insurance and finance:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht ; Boston ; Köln ; Tokyo
VSP
2002
|
| Series: | Modern probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 415 - 429 |
| Physical Description: | XIX, 434 S. |
| ISBN: | 9067643661 |
Staff View
MARC
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| adam_text | MODERN PROBABILITY AND STATISTICS GENERALIZED POISSON MODELS AND THEIR
APPLICATIONS IN INSURANCE AND FINANCE VLADIMIR E. BENINGAND VICTOR YU.
KOROLEV MOSCOW STATE UNIVERSITY ///VSP/// UTRECHT * BOSTON * KOLN *
TOKYO, 2002 CONTENTS FOREWORD IX PREFACE XIII 1 BASIC NOTIONS OF
PROBABILITY THEORY 1 1.1 RANDOM VARIABLES, THEIR DISTRIBUTIONS AND
MOMENTS 1 1.2 GENERATING AND CHARACTERISTIC FUNCTIONS 11 1.3 RANDOM
VECTORS. STOCHASTIC INDEPENDENCE 21 1.4 WEAK CONVERGENCE OF RANDOM
VARIABLES AND DISTRIBUTION FUNCTIONS ... 24 1.5 POISSON THEOREM 30 1.6
LAW OF LARGE NUMBERS. CENTRAL LIMIT THEOREM. STABLE LAWS 35 1.7 THE
BERRY*ESSEEN INEQUALITY 45 1.8 ASYMPTOTIC EXPANSIONS IN THE CENTRAL
LIMIT THEOREM 47 1.9 ELEMENTARY PROPERTIES OF RANDOM SUMS 56 1.10
STOCHASTIC PROCESSES 62 2 POISSON PROCESS 69 2.1 THE DEFINITION AND
ELEMENTARY PROPERTIES OF A POISSON PROCESS 69 2.2 POISSON PROCESS AS A
MODEL OF CHAOTIC DISPLACEMENT OF POINTS IN TIME . . 72 2.3 THE
ASYMPTOTIC NORMALITY OF A POISSON PROCESS 74 2.4 ELEMENTARY RAREFACTION
OF RENEWAL PROCESSES 76 3 CONVERGENCE OF SUPERPOSITIONS OF INDEPENDENT
STOCHASTIC PROCESSES 83 3.1 CHARACTERISTIC FEATURES OF THE PROBLEM 83
3.2 APPROXIMATION OF DISTRIBUTIONS OF RANDOMLY INDEXED RANDOM SEQUENCES
BY SPECIAL MIXTURES 85 3.3 THE TRANSFER THEOREM. RELATIONS BETWEEN THE
LIMIT LAWS FOR RANDOM SEQUENCES WITH RANDOM AND NON-RANDOM INDICES 89
3.4 NECESSARY AND SUFFICIENT CONDITIONS FOR THE CONVERGENCE OF
DISTRIBUTIONS OF RANDOM SEQUENCES WITH INDEPENDENT RANDOM INDICES 91 3.5
CONVERGENCE OF DISTRIBUTIONS OF RANDOMLY INDEXED SEQUENCES TO IDENTI-
FIABLE LOCATION OR SCALE MIXTURES. THE ASYMPTOTIC BEHAVIOR OF EXTREMAL
RANDOM SUMS 98 3.6 CONVERGENCE OF DISTRIBUTIONS OF RANDOM SUMS. THE
CENTRAL LIMIT THEOREM AND THE LAW OF LARGE NUMBERS FOR RANDOM SUMS 105
3.7 A GENERAL THEOREM ON THE ASYMPTOTIC BEHAVIOR OF SUPERPOSITIONS OF
IN- DEPENDENT STOCHASTIC PROCESSES 115 3.8 THE TRANSFER THEOREM FOR
RANDOM SUMS OF INDEPENDENT IDENTICALLY DIS- TRIBUTED RANDOM VARIABLES IN
THE DOUBLE ARRAY LIMIT SCHEME 117 COMPOUND POISSON DISTRIBUTIONS 123 4.1
MIXED AND COMPOUND POISSON DISTRIBUTIONS 123 4.2 DISCRETE COMPOUND
POISSON DISTRIBUTIONS 129 4.3 THE ASYMPTOTIC NORMALITY OF COMPOUND
POISSON DISTRIBUTIONS. THE BERRY-ESSEEN INEQUALITY FOR POISSON RANDOM
SUMS. NON-CENTRAL LYA- PUNOV FRACTIONS 133 4.4 ASYMPTOTIC EXPANSIONS FOR
COMPOUND POISSON DISTRIBUTIONS 139 4.5 THE ASYMPTOTIC EXPANSIONS FOR THE
QUANTILES OF COMPOUND POISSON DIS- TRIBUTIONS 151 4.6 EXPONENTIAL
INEQUALITIES FOR THE PROBABILITIES OF LARGE DEVIATIONS OF POIS- SON
RANDOM SUMS. AN ANALOG OF BERNSHTEIN-KOLMOGOROV INEQUALITY . . 155 4.7
THE APPLICATION OF ESSCHER TRANSFORMS TO THE APPROXIMATION OF THE TAILS
OF COMPOUND POISSON DISTRIBUTIONS 157 4.8 ESTIMATES OF CONVERGENCE RATE
IN LOCAL LIMIT THEOREMS FOR POISSON RANDOM SUMS 166 CLASSICAL RISK
PROCESSES 181 5.1 THE DEFINITION OF THE CLASSICAL RISK PROCESS. ITS
ASYMPTOTIC NORMALITY . . 181 5.2 THE POLLACZEK-KHINCHIN*BEEKMAN FORMULA
FOR THE RUIN PROBABILITY IN THE CLASSICAL RISK PROCESS 185 5.3
APPROXIMATIONS FOR THE RUIN PROBABILITY WITH SMALL SAFETY LOADING . . .
189 5.4 ASYMPTOTIC EXPANSIONS FORTHE RUIN PROBABILITY WITH SMALL SAFETY
LOADING 191 5.5 APPROXIMATIONS FOR THE RUIN PROBABILITY 203 5.6
ASYMPTOTIC APPROXIMATIONS FOR THE DISTRIBUTION OF THE SURPLUS IN GENERAL
RISK PROCESSES 213 5.7 A PROBLEM OF INVENTORY CONTROL 221 5.8
ANON-CLASSICAL PROBLEM OF OPTIMIZATION OF THE INITIAL CAPITAL 227 DOUBLY
STOCHASTIC POISSON PROCESSES (COX PROCESSES) 233 6.1 THE ASYMPTOTIC
BEHAVIOR OF RANDOM SUMS OF RANDOM INDICATORS 233 6.2 MIXED POISSON
PROCESSES 238 6.3 THE MODIFIED POLLACZEK-KHINCHIN-BEEKMAN FORMULA 249
6.4 THE DEFINITION AND ELEMENTARY PROPERTIES OF DOUBLY STOCHASTIC
POISSON PROCESSES 252 6.5 THE ASYMPTOTIC BEHAVIOR OF COX PROCESSES 256
COMPOUND COX PROCESSES WITH ZERO MEAN 265 7.1 DEFINITION. EXAMPLES 265
7.2 CONDITIONS OF CONVERGENCE OF THE DISTRIBUTIONS OF COMPOUND COX
PROCESS- ES WITH ZERO MEAN. LIMIT LAWS 266 7.3 CONVERGENCE RATE
ESTIMATES 269 7.4 ASYMPTOTIC EXPANSIONS FOR THE DISTRIBUTIONS OF
COMPOUND COX PROCESSES WITH ZERO MEAN 273 7.5 ASYMPTOTIC EXPANSIONS FOR
THE QUANTILES OF COMPOUND COX PROCESSES WITH ZERO MEAN 281 7.6
EXPONENTIAL INEQUALITIES FOR THE PROBABILITIES OF LARGE DEVIATIONS OF
COM- POUND COX PROCESSES WITH ZERO MEAN 283 VI 7.7 LIMIT THEOREMS FOR
EXTREMA OF COMPOUND COX PROCESSES WITH ZERO MEAN 285 7.8 ESTIMATES OF
THE RATE OF CONVERGENCE OF EXTREMA OF COMPOUND COX PRO- CESSES WITH ZERO
MEAN 287 8 MODELING EVOLUTION OF STOCK PRICES BY COMPOUND COX PROCESSES
291 8.1 INTRODUCTION 291 8.2 NORMAL AND STABLE MODELS 292 8.3
HETEROGENEITY OF OPERATIONAL TIME AND NORMAL MIXTURES 294 8.4
INHOMOGENEOUS DISCRETE CHAOS AND COX PROCESSES 297 8.5 RESTRICTION OF
THE CLASS OF MIXING DISTRIBUTIONS 303 8.6 HEAVY-TAILEDNESS OF SCALE
MIXTURES OF NORMALS 307 8.7 THE CASE OF ELEMENTARY INCREMENTS WITH
NON-ZERO MEANS 308 8.8 MODELS WITHIN THE DOUBLE ARRAY LIMIT SCHEME * . .
. 310 8.9 QUANTILES OF THE DISTRIBUTIONS OF STOCK PRICES 313 9 COMPOUND
COX PROCESSES WITH NONZERO MEAN 317 9.1 DEFINITION. EXAMPLES 317 9.2
CONDITIONS OF CONVERGENCE OF COMPOUND COX PROCESSES WITH NONZERO MEAN.
LIMIT LAWS 318 9.3 CONVERGENCE RATE ESTIMATES FOR COMPOUND COX PROCESSES
WITH NONZERO MEAN 322 9.4 ASYMPTOTIC EXPANSIONS FOR THE DISTRIBUTIONS OF
COMPOUND COX PROCESSES WITH NONZERO MEAN 326 9.5 ASYMPTOTIC EXPANSIONS
FOR THE QUANTILES OF COMPOUND COX PROCESSES WITH NONZERO MEAN 338 9.6
EXPONENTIAL INEQUALITIES FOR THE NEGATIVE VALUES OF THE SURPLUS IN
COLLEC- TIVE RISK MODELS WITH STOCHASTIC INTENSITY OF INSURANCE PAYMENTS
.... 339 9.7 LIMIT THEOREMS FOR EXTREMA OF COMPOUND COX PROCESSES WITH
NONZERO MEAN 342 9.8 CONVERGENCE RATE ESTIMATES FOR EXTREMA OF COMPOUND
COX PROCESSES WITH NONZERO MEAN 347 9.9 MINIMUM ADMISSIBLE RESERVE OF AN
INSURANCE COMPANY WITH STOCHASTIC INTENSITY OF INSURANCE PAYMENTS 350
9.10 OPTIMIZATION OF THE INITIAL CAPITAL OF AN INSURANCE COMPANY IN A
STATIC INSURANCE MODEL WITH RANDOM PORTFOLIO SIZE 351 10 FUNCTIONAL
LIMIT THEOREMS FOR COMPOUND COX PROCESSES 357 10.1 FUNCTIONAL LIMIT
THEOREMS FOR NON-CENTERED COMPOUND COX PROCESSES . . 357 10.2 FUNCTIONAL
LIMIT THEOREMS FOR NONRANDOMLY CENTERED COMPOUND COX PRO- CESSES 363 11
GENERALIZED RISK PROCESSES 373 . 11.1 THE DEFINITION OF GENERALIZED RISK
PROCESSES 373 11.2 CONDITIONS OF CONVERGENCE OF THE DISTRIBUTIONS OF
GENERALIZED RISK PRO- CESSES . 375 11.3 CONVERGENCE RATE ESTIMATES FOR
GENERALIZED RISK PROCESSES 378 11.4 ASYMPTOTIC EXPANSIONS FOR THE
DISTRIBUTIONS OF GENERALIZED RISK PROCESSES 381 11.5 ASYMPTOTIC
EXPANSIONS FOR THE QUANTILES OF GENERALIZED RISK PROCESSES . 384 11.6
EXPONENTIAL INEQUALITIES FOR THE PROBABILITIES OF NEGATIVE VALUES OF
GEN- ERALIZED RISK PROCESSES 386 VLL 12 STATISTICAL INFERENCE CONCERNING
THE PARAMETERS OF RISK PROCESSES 391 12.1 STATISTICAL ESTIMATION OF THE
RUIN PROBABILITY IN CLASSICAL RISK PROCESSES 391 12.2 SPECIFIC FEATURES
OF STATISTICAL ESTIMATION OF RUIN PROBABILITY FOR GENERAL- IZED RISK
PROCESSES 395 12.3 A NONPARAMETRIC ESTIMATOR OF THE RUIN PROBABILITY FOR
A GENERALIZED RISK PROCESS 398 12.4 INTERVAL ESTIMATOR OF THE RUIN
PROBABILITY FOR A GENERALIZED RISK PROCESS 404 12.5 COMPUTATIONAL
ASPECTS OF THE CONSTRUCTION OF CONFIDENCE INTERVALS FOR THE RUIN
PROBABILITY IN GENERALIZED RISK PROCESSES 412 BIBLIOGRAPHY 415 INDEX 431
VM
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| id | DE-604.BV014729684 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:05:34Z |
| institution | BVB |
| isbn | 9067643661 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009981972 |
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| physical | XIX, 434 S. |
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| publisher | VSP |
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| series2 | Modern probability and statistics |
| spelling | Bening, Vladimir E. Verfasser aut Generalized Poisson models and their applications in insurance and finance Vladimir E. Bening and Victor Yu. Korolev Utrecht ; Boston ; Köln ; Tokyo VSP 2002 XIX, 434 S. txt rdacontent n rdamedia nc rdacarrier Modern probability and statistics Literaturverz. S. 415 - 429 Bedrijfsfinanciering gtt Stochastische processen gtt Verzekeringswezen gtt Mathematisches Modell Finance Mathematical models Insurance Mathematical models Poisson distribution Poisson processes Poisson-Prozess (DE-588)4174971-6 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Poisson-Prozess (DE-588)4174971-6 s Versicherungsmathematik (DE-588)4063194-1 s DE-604 Finanzmathematik (DE-588)4017195-4 s Korolev, Viktor Ju. Verfasser (DE-588)124630936 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981972&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bening, Vladimir E. Korolev, Viktor Ju Generalized Poisson models and their applications in insurance and finance Bedrijfsfinanciering gtt Stochastische processen gtt Verzekeringswezen gtt Mathematisches Modell Finance Mathematical models Insurance Mathematical models Poisson distribution Poisson processes Poisson-Prozess (DE-588)4174971-6 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4174971-6 (DE-588)4063194-1 (DE-588)4017195-4 |
| title | Generalized Poisson models and their applications in insurance and finance |
| title_auth | Generalized Poisson models and their applications in insurance and finance |
| title_exact_search | Generalized Poisson models and their applications in insurance and finance |
| title_full | Generalized Poisson models and their applications in insurance and finance Vladimir E. Bening and Victor Yu. Korolev |
| title_fullStr | Generalized Poisson models and their applications in insurance and finance Vladimir E. Bening and Victor Yu. Korolev |
| title_full_unstemmed | Generalized Poisson models and their applications in insurance and finance Vladimir E. Bening and Victor Yu. Korolev |
| title_short | Generalized Poisson models and their applications in insurance and finance |
| title_sort | generalized poisson models and their applications in insurance and finance |
| topic | Bedrijfsfinanciering gtt Stochastische processen gtt Verzekeringswezen gtt Mathematisches Modell Finance Mathematical models Insurance Mathematical models Poisson distribution Poisson processes Poisson-Prozess (DE-588)4174971-6 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Bedrijfsfinanciering Stochastische processen Verzekeringswezen Mathematisches Modell Finance Mathematical models Insurance Mathematical models Poisson distribution Poisson processes Poisson-Prozess Versicherungsmathematik Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981972&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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