Journal article
An elementary derivation of Hattendorff’s theorem
European actuarial journal, Vol.11(1), pp.319-323
01/05/2021
DOI: 10.1007/s13385-020-00256-9
Abstract
For a general fully continuous life insurance model, the variance of the loss-at-issue random variable is the expectation of the square of the discounted value of the net amount at risk at the moment of death. In 1964 Jim Hickman gave an elementary and elegant derivation of this result by the method of integration by parts. One might expect that the method of summation by parts could be used to treat the fully discrete case. However, there are two difficulties. The summation-by-parts formula involves shifting an index, making it somewhat unwieldy. In the fully discrete case, the variance of the loss-at-issue random variable is more complicated; it is the expectation of the square of the discounted value of the net amount at risk at the end of the year of death times a survival probability factor. The purpose of this note is to show that one can indeed use the method of summation by parts to find the variance of the loss-at-issue random variable for a fully discrete life insurance policy.
Details
- Title: Subtitle
- An elementary derivation of Hattendorff’s theorem
- Creators
- Elias S. W Shiu - University of IowaXiaoyi Xiong - Transamerica Life Insurance Company, Plano, USA
- Resource Type
- Journal article
- Publication Details
- European actuarial journal, Vol.11(1), pp.319-323
- DOI
- 10.1007/s13385-020-00256-9
- ISSN
- 2190-9733
- eISSN
- 2190-9741
- Publisher
- Springer Berlin Heidelberg
- Language
- English
- Date published
- 01/05/2021
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257635002771
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