Lundberg Approximations for Compound Distributions with Insurance Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2001
|
| Schriftenreihe: | Lecture Notes in Statistics
156 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is inductive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound distributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexponential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed |
| Beschreibung: | 1 Online-Ressource (X, 250p) |
| ISBN: | 9781461301110 9780387951355 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4613-0111-0 |
Internformat
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Datensatz im Suchindex
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| issn | 0930-0325 |
| language | English |
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| spelling | Willmot, Gordon E. Verfasser aut Lundberg Approximations for Compound Distributions with Insurance Applications by Gordon E. Willmot, X. Sheldon Lin New York, NY Springer New York 2001 1 Online-Ressource (X, 250p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 156 0930-0325 These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is inductive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound distributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexponential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed Mathematics Finance Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Statistics for Business/Economics/Mathematical Finance/Insurance Quantitative Finance Mathematik Statistik Wirtschaft Zusammengesetzte Verteilung (DE-588)4191153-2 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Zusammengesetzte Verteilung (DE-588)4191153-2 s Approximation (DE-588)4002498-2 s 1\p DE-604 Lin, X. Sheldon Sonstige oth Lecture Notes in Statistics 156 (DE-604)BV036592911 156 https://doi.org/10.1007/978-1-4613-0111-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Willmot, Gordon E. Lundberg Approximations for Compound Distributions with Insurance Applications Lecture Notes in Statistics Mathematics Finance Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Statistics for Business/Economics/Mathematical Finance/Insurance Quantitative Finance Mathematik Statistik Wirtschaft Zusammengesetzte Verteilung (DE-588)4191153-2 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4191153-2 (DE-588)4002498-2 |
| title | Lundberg Approximations for Compound Distributions with Insurance Applications |
| title_auth | Lundberg Approximations for Compound Distributions with Insurance Applications |
| title_exact_search | Lundberg Approximations for Compound Distributions with Insurance Applications |
| title_full | Lundberg Approximations for Compound Distributions with Insurance Applications by Gordon E. Willmot, X. Sheldon Lin |
| title_fullStr | Lundberg Approximations for Compound Distributions with Insurance Applications by Gordon E. Willmot, X. Sheldon Lin |
| title_full_unstemmed | Lundberg Approximations for Compound Distributions with Insurance Applications by Gordon E. Willmot, X. Sheldon Lin |
| title_short | Lundberg Approximations for Compound Distributions with Insurance Applications |
| title_sort | lundberg approximations for compound distributions with insurance applications |
| topic | Mathematics Finance Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Statistics for Business/Economics/Mathematical Finance/Insurance Quantitative Finance Mathematik Statistik Wirtschaft Zusammengesetzte Verteilung (DE-588)4191153-2 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Mathematics Finance Distribution (Probability theory) Economics / Statistics Probability Theory and Stochastic Processes Statistics for Business/Economics/Mathematical Finance/Insurance Quantitative Finance Mathematik Statistik Wirtschaft Zusammengesetzte Verteilung Approximation |
| url | https://doi.org/10.1007/978-1-4613-0111-0 |
| volume_link | (DE-604)BV036592911 |
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