The Investigation of a Forward-Rate Mortality Framework

Daniel H. Alai, Katja Ignatieva and Michael Sherris
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Daniel H. Alai: School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK
Katja Ignatieva: CEPAR, Risk and Actuarial Studies, UNSW Business School, UNSW, Sydney, NSW 2052, Australia
Michael Sherris: CEPAR, Risk and Actuarial Studies, UNSW Business School, UNSW, Sydney, NSW 2052, Australia

Risks, 2019, vol. 7, issue 2, 1-22

Abstract: 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.

Keywords: longevity risk; Olivier–Smith model; forward-rate mortality framework; minimum covariance pattern; copulas (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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