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Erschienen in: European Actuarial Journal 2/2018

12.06.2018 | Original Research Paper

The impact of longevity and investment risk on a portfolio of life insurance liabilities

verfasst von: Anna Rita Bacinello, Pietro Millossovich, An Chen

Erschienen in: European Actuarial Journal | Ausgabe 2/2018

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Abstract

In this paper we assess the joint impact of biometric and financial risk on the market valuation of life insurance liabilities. We consider a stylized, contingent claim based model of a life insurance company issuing participating contracts and subject to default risk, as pioneered by Briys and de Varenne (Geneva Pap Risk Insur Theory 19(1):53–72, 1994, J Risk Insur 64(4):673–694, 1997), and build on their model by explicitly introducing biometric risk and its components, namely diversifiable and systematic risk. The contracts considered include pure endowments, deferred whole life annuities and guaranteed annuity options. Our results stress the predominance of systematic over diversifiable risk in determining fair participation rates. We investigate the interaction of contract design, market regimes and mortality assumptions, and show that, particularly for lifelong benefits, the choice of the participation rate must be very conservative if longevity improvements are foreseeable.

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Fußnoten
1
The probability that a portfolio be completely extinct at maturity is negligible for usual ages and maturities and reasonable portfolio sizes. For instance, with a survival probability of \(95\%\) (which may be common for a 40-years old policyholder and a 20 years horizon), the probability of extinction is less than \(10^{-6}\) for a group of 5 individuals. When the survival probability is only \(50\%\), the extinction probability is less than \(10^{-6}\) for a group of 20 individuals.
 
2
Note that the indicator of the event \({\{N>0\}}\) can be omitted in presence of the indicator of the event \(\{\tau ^i>T\}\).
 
3
The function m is nonnegative, continuous, and satisfies \(\int _0^{+\infty } m(u)\text {d}u=+\infty \).
 
4
Formally, the random variable \(\Delta \) is measurable with respect to the \(\sigma \)-algebra containing the information available to market participants at time T.
 
5
This result also holds under any probability measure equivalent to Q, in particular under the physical measure.
 
6
See for instance [11, 12].
 
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Metadaten
Titel
The impact of longevity and investment risk on a portfolio of life insurance liabilities
verfasst von
Anna Rita Bacinello
Pietro Millossovich
An Chen
Publikationsdatum
12.06.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
European Actuarial Journal / Ausgabe 2/2018
Print ISSN: 2190-9733
Elektronische ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-018-0175-5

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