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Size-biased risk measures of compound sums

Recurso electrónico / Electronic resource
MARC record
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003  MAP
005  20210104134910.0
008  201228e20201201usa|||p |0|||b|eng d
040  ‎$a‎MAP‎$b‎spa‎$d‎MAP
084  ‎$a‎6
1001 ‎$0‎MAPA20080096434‎$a‎Denuit, Michel
24510‎$a‎Size-biased risk measures of compound sums‎$c‎Michel Denuit
520  ‎$a‎The size-biased, or length-biased transform is known to be particularly useful in insurance risk measurement. The case of continuous losses has been extensively considered in the actuarial literature. Given their importance in insurance studies, this article concentrates on compound sums. The zero-augmented distributions that naturally appear in the individual model of risk theory are obtained as particular cases when the claim frequency distribution is concentrated on {0, 1}. The general results derived in this article help actuaries to understand how risk measurement proceeds because the formulas make explicit the loadings corresponding to each source of randomness. Some simple and explicit expressions are obtained when losses are modeled by independent compound Poisson sums and compound mixed Poisson sums, including the compound negative binomial sums. Extensions to correlated risks are briefly discussed in the concluding section.
650 4‎$0‎MAPA20080579258‎$a‎Cálculo actuarial
650 4‎$0‎MAPA20080582951‎$a‎Teoría del riesgo
650 4‎$0‎MAPA20090041721‎$a‎Distribución Poisson-Beta
650 4‎$0‎MAPA20080602437‎$a‎Matemática del seguro
7730 ‎$w‎MAP20077000239‎$t‎North American actuarial journal‎$d‎Schaumburg : Society of Actuaries, 1997-‎$x‎1092-0277‎$g‎01/12/2020 Tomo 24 Número 4 - 2020 , p. 512-532