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12

Life and death questions

Open-access content Thursday 4th December 2014 — updated 4.50pm, Tuesday 14th April 2020
2

I have a few technical queries around the article Risks of mis-estimating mortality by Stephen Richards (The Actuary, November).

I thought that the article was very well written and useful, particularly around Solvency II and risk pricing.

First, on the correlations between the two parameters:

• Were these calculated from the data? If so, do you think some of the very small values (for example -1%) are spurious and should be modified to zero?

Richards: They were calculated from the log-likelihood, which itself was calibrated to the experience data. So, the data is involved, but indirectly, via its contribution to the log-likelihood.

The small values certainly support the assertion that some parameters are uncorrelated. Whether you set these to zero, or whether you use them unmodified, will make very little difference.

• Do you believe that correlations between the parameters would vary by scheme? It seems more intuitive to me that these correlations should be a feature of mortality, and not vary by scheme, whereas the actual parameter values themselves should vary by scheme. If so, do you think these could be set using a much larger dataset?

Richards: Yes, because different portfolios exhibit different correlations (and often different risk factors).

Second, on the generation of parameter sets for each portfolio valuation:

• Did you generate these assuming that the parameters formed a multi-variate normal distribution?

Richards: Yes. This assumption is well-grounded for joint maximum-likelihood estimators.

• Do you think a copula-type approach, potentially allowing for tail dependence, could give different 

results and do you think this could be more appropriate?

Richards: It would give different results, but I don't think it would be more appropriate. The multi-variate normal distribution assumption is a well-founded asymptotic feature of maximum-likelihood estimators.


Matthew Roche 

17 November


This article appeared in our December 2014 issue of The Actuary.
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