Gerber-Shiu risk theory:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham [u.a.]
Springer
2013
|
| Schriftenreihe: | EAA series
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026911694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 91 - 93 |
| Umfang: | VIII, 93 S. graph. Darst. |
| ISBN: | 9783319023021 9783319023038 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819305335926554624 |
|---|---|
| adam_text | Titel: Gerber-Shiu risk theory
Autor: Kyprianou, Andreas E
Jahr: 2013
Contents
1 Introduction..............................................................1
1.1 The Cramér-Lundberg Process....................................1
1.2 The Classical Problem of Ruin ....................................3
1.3 Gerber-Shiu Expected Discounted Penalty Functions ............4
1.4 Exotic Gerber-Shiu Theory........................................5
1.5 Comments..........................................................7
2 The Wald Martingale and the Maximum..............................9
2.1 Laplace Exponent..................................................9
2.2 First Exponential Martingale ......................................1 ]
2.3 Esscher Transform..................................................12
2.4 Distribution of the Maximum......................................14
2.5 Comments..........................................................15
3 The Kella-Whitt Martingale and the Minimum......................17
3.1 The Cramér-Lundberg Process Reflected in Its Supremum . ... 17
3.2 A Useful Poisson Integral..........................................18
3.3 Second Exponential Martingale....................................21
3.4 Duality..............................................................22
3.5 Distribution of the Minimum......................................24
3.6 The Long-Term Behaviour..........................................25
3.7 Comments..........................................................25
4 Scale Functions and Ruin Probabilities................................27
4.1 Scale Functions and the Probability of Ruin ......................27
4.2 Connection with the Pollaczek-Khintchine Formula..............30
4.3 Gambler s Ruin....................................................33
4.4 Comments..........................................................35
5 The Gerber-Shiu Measure....................................37
5.1 Decomposing Paths at the Minimum..............................37
5.2 Resolvent Densities................................................38
vii
viii Contents
5.3 More on Poisson Integrals..........................................40
5.4 Gerber-Shiu Measure and Gambler s Ruin........................41
5.5 Comments..........................................................43
6 Reflection Strategies....................................................45
6.1 Perpetuities..........................................................46
6.2 Decomposing Paths at the Maximum..............................47
6.3 Derivative of the Scale Function....................................51
6.4 Present Value of Dividends Paid Until Ruin........................53
6.5 Comments..........................................................54
7 Perturbation-at-Maximum Strategies..................................57
7.1 Rehung Excursions ................................................57
7.2 Marked Poisson Process Revisited ................................59
7.3 Gambler s Ruin for the Perturbed Process..........................61
7.4 Continuous Ruin with Heavy Perturbation ........................63
7.5 Expected Present Value of Tax at Ruin............................64
7.6 Comments..........................................................65
8 Refraction Strategies....................................................67
8.1 Pathwise Existence and Uniqueness................................67
8.2 Gambler s Ruin and Resolvent Density............................70
8.3 Resolvent Density with Ruin ......................................75
8.4 Comments..........................................................77
9 Concluding Discussion..................................................79
9.1 Mixed-Exponential Claims ........................................79
9.2 Spectrally Negative Lévy Processes................................81
9.3 Analytic Properties of Scale Functions............................84
9.4 Engineered Scale Functions........................................85
9.5 Comments..........................................................89
References.......................91
|
| any_adam_object | 1 |
| author | Kyprianou, Andreas E. |
| author_facet | Kyprianou, Andreas E. |
| author_role | aut |
| author_sort | Kyprianou, Andreas E. |
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| building | Verbundindex |
| bvnumber | BV041465434 |
| classification_rvk | SK 820 SK 980 |
| ctrlnum | (OCoLC)863147994 (DE-599)GBV770507387 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041465434 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:47:59Z |
| institution | BVB |
| isbn | 9783319023021 9783319023038 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026911694 |
| oclc_num | 863147994 |
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| owner | DE-11 DE-188 |
| owner_facet | DE-11 DE-188 |
| physical | VIII, 93 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | EAA series |
| spellingShingle | Kyprianou, Andreas E. Gerber-Shiu risk theory Risikotheorie (DE-588)4135592-1 gnd |
| subject_GND | (DE-588)4135592-1 |
| title | Gerber-Shiu risk theory |
| title_auth | Gerber-Shiu risk theory |
| title_exact_search | Gerber-Shiu risk theory |
| title_full | Gerber-Shiu risk theory Andreas E. Kyprianou |
| title_fullStr | Gerber-Shiu risk theory Andreas E. Kyprianou |
| title_full_unstemmed | Gerber-Shiu risk theory Andreas E. Kyprianou |
| title_short | Gerber-Shiu risk theory |
| title_sort | gerber shiu risk theory |
| topic | Risikotheorie (DE-588)4135592-1 gnd |
| topic_facet | Risikotheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026911694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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