key: cord-1017299-gtcin9tj
authors: Boumezoued, Alexandre
title: Discussion on “Exchangeable mortality projection” (Shapovalov et al.)
date: 2021-06-11
journal: Eur Actuar J
DOI: 10.1007/s13385-021-00286-x
sha: 679f73654631ee386baa3851ee9f19bc7096b6f2
doc_id: 1017299
cord_uid: gtcin9tj

nan

this context is to achieve a joint quantification of both process and estimation errors in a coherent framework.

Czado et al. [1] led the way to such a quantification in the context of a Lee-Carter model. In the present paper, Shapovalov et al. provide an extension of this original work in two directions, namely capturing the joint dynamics of multiple populations, and allowing exchangeability between parameters of different populations, following the theory developed by Gill [2] . Exchangeability can be seen as a more general form of the traditional assumption of "independent and identically distributed" random variables.

Shapovalov et al. (2021) apply the theory of exchangeability to the parameters driving the mortality dynamics of the different population groups. This framework is used to build a hierarchical model where the distribution of the population-specific parameters depends on a common hyper-parameter (itself stochastic). In this setting, the paper develops the posterior distributions of the model parameters. The virtue of the approach can be seen, as the overall modelling is unified: in particular, the time series inference is included in the overall model, as opposed to the traditional frequentist approach to stochastic mortality modelling; also, the inference process is based on a balance between population-specific information and the joint knowledge from all populations.

In the past literature, the use of multi-population models may have appeared challenging in some instances, in particular when one assesses the obtained accuracy in comparison to classical single-population models. This could be partly due to the fact that the multi-population is imposing an additional structure on the behavior of the two or more countries, which therefore results into more constraints in the forecast. To counterbalance the effect, the relevance of the specification of the multipopulation model combined with the additional population mortality information must add value to the overall prediction power.

The authors demonstrate that the forecasting accuracy can benefit from the exchangeability assumption between populations in comparison to the standard Bayesian single-population approach. Such a result is interesting for practitioners as it reminds us that the problem of mortality and longevity risks quantification for a given population can take advantage of including information on other population groups or countries. In doing so, the modeler is able to improve forecasts or alternatively reduce risk, as opposed to considering single population models solely.

Recalling that the Bayesian approach allows to quantify both process and estimation errors coherently, the method proposed in the present paper appears as a promising toolbox for the quantification of mortality and longevity risks. As shown by the Solvency II and IFRS 17 requirements, this quantification is of specific importance to financial measurement and disclosure of long term insurance risks, by taking into account parameter uncertainty while leveraging wider information on other populations.

There are a number of open challenges related to the modelling of multiple populations, including how the country groups are designed. The present paper advocates to rely on statistical criteria to derive population pairing strategies as opposed to linking populations based on similar characteristics (e.g. demographic or economic). This is to us an interesting idea, expanding the scope of possible data that can be leveraged, which would need to be further explored to propose a systematic method to grouping multiple populations.

The COVID-19 crisis has shown how difficult it is to anticipate mortality deviations in general and reminds us that the quantification of mortality and longevity risks remain a challenging task. As another example, the long term mortality impact of climate-related risks is, by nature, uncertain. Regulatory scrutiny is increasing towards the proper quantification of those risks in view of further improving the awareness and stability of the insurance sector. This leaves the way for leveraging the information embedded in the joint evolution of population mortality worldwide for better risk assessment and forecasting.

Bayesian Poisson log-bilinear mortality projections

Bayesian methods: a social and behavioral sciences approach

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.