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The Investigation of a Forward-Rate Mortality Framework

School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK
CEPAR, Risk and Actuarial Studies, UNSW Business School, UNSW, Sydney, NSW 2052, Australia
Author to whom correspondence should be addressed.
Risks 2019, 7(2), 61;
Received: 13 February 2019 / Revised: 10 April 2019 / Accepted: 15 May 2019 / Published: 1 June 2019
Stochastic mortality models have been developed for a range of applications from demographic projections to financial management. Financial risk based models built on methods used for interest rates and apply these to mortality rates. They have the advantage of being applied to financial pricing and the management of longevity risk. Olivier and Jeffery (2004) and Smith (2005) proposed a model based on a forward-rate mortality framework with stochastic factors driven by univariate gamma random variables irrespective of age or duration. We assess and further develop this model. We generalize random shocks from a univariate gamma to a univariate Tweedie distribution and allow for the distributions to vary by age. Furthermore, since dependence between ages is an observed characteristic of mortality rate improvements, we formulate a multivariate framework using copulas. We find that dependence increases with age and introduce a suitable covariance structure, one that is related to the notion of ax minimum. The resulting model provides a more realistic basis for capturing the risk of mortality improvements and serves to enhance longevity risk management for pension and insurance funds. View Full-Text
Keywords: longevity risk; Olivier–Smith model; forward-rate mortality framework; minimum covariance pattern; copulas longevity risk; Olivier–Smith model; forward-rate mortality framework; minimum covariance pattern; copulas
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Alai, D.H.; Ignatieva, K.; Sherris, M. The Investigation of a Forward-Rate Mortality Framework. Risks 2019, 7, 61.

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