Size-Biased Risk Measures of Compound Sums

Michel Denuit ()
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Michel Denuit: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2020034, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: The 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.

Keywords: Weighted risk measures; Conditional tail expectation; Panjer recursion; Compound Poisson distribution; Compound mixed Poisson distribution; Infinite divisibility; Common mixture model (search for similar items in EconPapers)
Date: 2020-12-18
Note: In: North American Actuarial Journal - Vol. 24, no.4, p. 512-532 (2020)
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020034

DOI: 10.1080/10920277.2019.1676787

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