Stochastic Mortality: The Impact on Target Capital

University Bocconi - CAREFIN Working Paper

22 Pages Posted: 22 Oct 2008 Last revised: 23 Sep 2009

See all articles by Annamaria Olivieri

Annamaria Olivieri

University of Parma - Dipartimento di Scienze Economiche e Aziendali

Ermanno Pitacco

MIB Trieste School of Management

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Date Written: October 20, 2008


In this paper, we take the point of view of an insurer dealing with life annuities, which aims at building up a (partial) internal model in order to quantify the impact of mortality risks, namely process and longevity risk, in view of taking appropriate risk management actions. We assume that a life table, providing a best-estimate assessment of annuitants' future mortality is available; conversely, no access to data sets and the methodology underlying the construction of the life table is at the insurer's disposal. In spite of this, a stochastic approach is required.

We focus on the annual number of deaths in a given cohort, which we model allowing for a random mortality rate. To this purpose, we extend the widely used Poisson model, first assuming a Gamma-distributed random parameter, and second introducing time-dependence in the parameter itself. Further, we define a Bayesian-inferential procedure for updating the parameters to experience in some situations. The setting we define does not demand advanced analytical tools, while allowing for process and longevity risk in a rigorous way.

The model is then implemented for capital allocation purposes. We investigate the amount of the required capital for a given life annuity portfolio, based on solvency targets which could be adopted within internal models. The outcomes of such an investigation are compared with the capital required according to some standard rules, in particular those proposed within the Solvency 2 project.

Keywords: Life annuities, Random fluctuations, Systematic deviations, Process risk, Longevity risk, Solvency, Insurance risk management, Internal models

JEL Classification: G22

Suggested Citation

Olivieri, Annamaria and Pitacco, Ermanno, Stochastic Mortality: The Impact on Target Capital (October 20, 2008). University Bocconi - CAREFIN Working Paper, Available at SSRN: or

Annamaria Olivieri (Contact Author)

University of Parma - Dipartimento di Scienze Economiche e Aziendali ( email )

via Kennedy 6
Parma, 43125

Ermanno Pitacco

MIB Trieste School of Management

Trieste, Trieste 34100

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