An elementary derivation of Hattendorff's theorem
Objetos digitales
| Tag | 1 | 2 | Value |
|---|---|---|---|
| LDR | 00000cab a2200000 4500 | ||
| 001 | MAP20220007276 | ||
| 003 | MAP | ||
| 005 | 20220301102646.0 | ||
| 008 | 220301e20210607esp|||p |0|||b|spa d | ||
| 040 | $aMAP$bspa$dMAP | ||
| 084 | $a6 | ||
| 100 | 1 | $0MAPA20220002240$aShiu, Elias S. W. | |
| 245 | 1 | 0 | $aAn elementary derivation of Hattendorff's theorem$cElias S. W. Shiu, Xiaoyi Xiong |
| 520 | $aFor 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. | ||
| 540 | $aLa copia digital se distribuye bajo licencia "Attribution 4.0 International (CC BY 4.0)"$f$uhttps://creativecommons.org/licenses/by/4.0$943 | ||
| 650 | 4 | $0MAPA20080550417$aDerivados | |
| 650 | 4 | $0MAPA20080616106$aCálculo de probabilidades | |
| 650 | 4 | $0MAPA20080579258$aCálculo actuarial | |
| 700 | 1 | $0MAPA20220002257$aXiong , Xiaoyi | |
| 773 | 0 | $wMAP20220007085$tEuropean Actuarial Journal$dCham, Switzerland : Springer Nature Switzerland AG, 2021-2022$g07/06/2021 Número 1 - junio 2021 , p. 319-323 | |
| 856 | $qapplication/pdf$w1114384$yRecurso electrónico / Electronic resource |