Overview
- Authors:
-
-
Gordon E. Willmot
-
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
-
X. Sheldon Lin
-
Department of Statistics and Actuarial Science, University of Iowa, Iowa City, USA
Access this book
Other ways to access
Table of contents (11 chapters)
-
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 1-5
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 7-36
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 37-49
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 51-80
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 81-91
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 93-105
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 107-140
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 141-149
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 151-181
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 183-208
-
- Gordon E. Willmot, X. Sheldon Lin
Pages 209-234
-
Back Matter
Pages 235-252
About this book
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 induc tive, 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 dis tributions 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 nonexpo nential 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.
Authors and Affiliations
-
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
Gordon E. Willmot
-
Department of Statistics and Actuarial Science, University of Iowa, Iowa City, USA
X. Sheldon Lin
