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**Mortality-dependent financial risk measures.**
*(English)*
Zbl 1168.91411

Summary: This paper uses a recently developed two-factor stochastic mortality model to estimate financial risk measures for four illustrative types of mortality-dependent financial position: investments in zero-coupon longevity bonds; investments in longevity bonds that pay annual survivor-dependent coupons; and two examples of an insurer’s annuity book that are each hedged by a longevity bond, one based on the annuity book and hedge having the same reference cohort, and the other not. The risk measures estimated are the value-at-risk, the expected shortfall and a spectral risk measure based on an exponential risk-aversion function. Results are reported on a model calibrated on data provided by the UK Government Actuary’s Department, both with and without underlying parameter uncertainty.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

91B82 | Statistical methods; economic indices and measures |

91B28 | Finance etc. (MSC2000) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

### Keywords:

mortality risk; longevity bonds; value-at-risk; coherent risk measures; spectral risk measures### Software:

Dowd
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\textit{K. Dowd} et al., Insur. Math. Econ. 38, No. 3, 427--440 (2006; Zbl 1168.91411)

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