Abstract
Abstract The COVID-19 pandemic creates a challenge for actuaries analysing experience data that include mortality shocks. Without sufficient local flexibility in the time dimension, any analysis based on the most recent data will be biased by the temporarily higher mortality. Also, depending on where the shocks sit in the exposure period, any attempt to identify mortality trends will be distorted. We present a methodology for analysing portfolio mortality data that offer local flexibility in the time dimension. The approach permits the identification of seasonal variation, mortality shocks and occurred-but-not reported deaths (OBNR). The methodology also allows actuaries to measure portfolio-specific mortality improvements. Finally, the method assists actuaries in determining a representative mortality level for long-term applications like reserving and pricing, even in the presence of mortality shocks. Results are given for a mature annuity portfolio in the UK, which suggest that the Bayesian information criterion is better for actuarial model selection in this application than Akaike’s information criterion.
Highlights
The COVID-19 pandemic creates a challenge for actuaries analysing experience data that include mortality shocks
Results are given for a mature annuity portfolio in the UK, which suggest that the Bayesian information criterion is better for actuarial model selection in this application than Akaike’s information criterion
Epidemiology Team, 2020) creates the need to allow for mortality shocks in experience analysis performed by actuaries
Summary
Epidemiology Team, 2020) creates the need to allow for mortality shocks in experience analysis performed by actuaries. We use two kinds of spline: Hermite splines, which span the interval [0,1], and Schoenberg (1964) splines, which are piecewise local polynomials on the real line. The plan of the rest of this paper is as follows: section 2 presents important features of COVID19 mortality in the UK and the resulting need for continuous time methods in place of annual qx rates; section 3 describes the data set used in the paper; section 4 describes the use of Hermite splines for modelling mortality by age, while section 5 describes how to use Hermite splines for modelling mortality by annuity amount.
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