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12 pages, 5299 KiB

Open AccessArticle

Bayesian Mixture Modelling for Mortality Projection

by Jackie Li and Atsuyuki Kogure

Risks 2021, 9(4), 76; https://doi.org/10.3390/risks9040076 - 15 Apr 2021

Cited by 1 | Viewed by 2460

Although a large number of mortality projection models have been proposed in the literature, relatively little attention has been paid to a formal assessment of the effect of model uncertainty. In this paper, we construct a Bayesian framework for embedding more than one [...] Read more.

Although a large number of mortality projection models have been proposed in the literature, relatively little attention has been paid to a formal assessment of the effect of model uncertainty. In this paper, we construct a Bayesian framework for embedding more than one mortality projection model and utilise the finite mixture model concept to allow for the blending of model structures. Under this framework, the varying features of different model structures can be exploited jointly and coherently to have a more detailed description of the underlying mortality patterns. We show that the proposed Bayesian approach performs well in fitting and forecasting Japanese mortality. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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10 pages, 416 KiB

Open AccessArticle

Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models

by Anthony Medford

Risks 2021, 9(3), 51; https://doi.org/10.3390/risks9030051 - 10 Mar 2021

Cited by 1 | Viewed by 2384

Abstract

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework [...] Read more.

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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32 pages, 12746 KiB

Open AccessArticle

Clustering-Based Extensions of the Common Age Effect Multi-Population Mortality Model

by Simon Schnürch, Torsten Kleinow and Ralf Korn

Risks 2021, 9(3), 45; https://doi.org/10.3390/risks9030045 - 1 Mar 2021

Cited by 11 | Viewed by 3221

Abstract

We introduce four variants of the common age effect model proposed by Kleinow, which describes the mortality rates of multiple populations. Our model extensions are based on the assumption of multiple common age effects, each of which is shared only by a subgroup [...] Read more.

We introduce four variants of the common age effect model proposed by Kleinow, which describes the mortality rates of multiple populations. Our model extensions are based on the assumption of multiple common age effects, each of which is shared only by a subgroup of all considered populations. This makes the models more realistic while still keeping them as parsimonious as possible, improving the goodness of fit. We apply different clustering methods to identify suitable subgroups. Some of the algorithms are borrowed from the unsupervised learning literature, while others are more domain-specific. In particular, we propose and investigate a new model with fuzzy clustering, in which each population’s individual age effect is a linear combination of a small number of age effects. Due to their good interpretability, our clustering-based models also allow some insights in the historical mortality dynamics of the populations. Numerical results and graphical illustrations of the considered models and their performance in-sample as well as out-of-sample are provided. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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19 pages, 530 KiB

Open AccessEditor’s ChoiceArticle

Mortality Forecasting with an Age-Coherent Sparse VAR Model

by Hong Li and Yanlin Shi

Risks 2021, 9(2), 35; https://doi.org/10.3390/risks9020035 - 5 Feb 2021

Cited by 12 | Viewed by 3029

Abstract

This paper proposes an age-coherent sparse Vector Autoregression mortality model, which combines the appealing features of existing VAR-based mortality models, to forecast future mortality rates. In particular, the proposed model utilizes a data-driven method to determine the autoregressive coefficient matrix, and then employs [...] Read more.

This paper proposes an age-coherent sparse Vector Autoregression mortality model, which combines the appealing features of existing VAR-based mortality models, to forecast future mortality rates. In particular, the proposed model utilizes a data-driven method to determine the autoregressive coefficient matrix, and then employs a rotation algorithm in the projection phase to generate age-coherent mortality forecasts. In the estimation phase, the age-specific mortality improvement rates are fitted to a VAR model with dimension reduction algorithms such as the elastic net. In the projection phase, the projected mortality improvement rates are assumed to follow a short-term fluctuation component and a long-term force of decay, and will eventually converge to an age-invariant mean in expectation. The age-invariance of the long-term mean guarantees age-coherent mortality projections. The proposed model is generalized to multi-population context in a computationally efficient manner. Using single-age, uni-sex mortality data of the UK and France, we show that the proposed model is able to generate more reasonable long-term projections, as well as more accurate short-term out-of-sample forecasts than popular existing mortality models under various settings. Therefore, the proposed model is expected to be an appealing alternative to existing mortality models in insurance and demographic analyses. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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18 pages, 2680 KiB

Open AccessArticle

A Study on Link Functions for Modelling and Forecasting Old-Age Survival Probabilities of Australia and New Zealand

by Jacie Jia Liu

Risks 2021, 9(1), 11; https://doi.org/10.3390/risks9010011 - 2 Jan 2021

Cited by 2 | Viewed by 2558

Abstract

Forecasting survival probabilities and life expectancies is an important exercise for actuaries, demographers, and social planners. In this paper, we examine extensively a number of link functions on survival probabilities and model the evolution of period survival curves of lives aged 60 over [...] Read more.

Forecasting survival probabilities and life expectancies is an important exercise for actuaries, demographers, and social planners. In this paper, we examine extensively a number of link functions on survival probabilities and model the evolution of period survival curves of lives aged 60 over time for the elderly populations in Australasia. The link functions under examination include the newly proposed gevit and gevmin, which are compared against the traditional ones like probit, complementary log-log, and logit. We project the model parameters and so the survival probabilities into the future, from which life expectancies at old ages can be forecasted. We find that some of these models on survival probabilities, particularly those based on the new links, can provide superior fitting results and forecasting performances when compared to the more conventional approach of modelling mortality rates. Furthermore, we demonstrate how these survival probability models can be extended to incorporate extra explanatory variables such as macroeconomic factors in order to further improve the forecasting performance. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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18 pages, 1513 KiB

Open AccessArticle

Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect

by Karim Barigou, Stéphane Loisel and Yahia Salhi

Risks 2021, 9(1), 5; https://doi.org/10.3390/risks9010005 - 24 Dec 2020

Cited by 5 | Viewed by 3291

Abstract

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Standard single population models typically suffer from two major drawbacks: on the one hand, they use a large number of parameters compared to the sample size and, [...] Read more.

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Standard single population models typically suffer from two major drawbacks: on the one hand, they use a large number of parameters compared to the sample size and, on the other hand, model choice is still often based on in-sample criterion, such as the Bayes information criterion (BIC), and therefore not on the ability to predict. In this paper, we develop a model based on a decomposition of the mortality surface into a polynomial basis. Then, we show how regularization techniques and cross-validation can be used to obtain a parsimonious and coherent predictive model for mortality forecasting. We analyze how COVID-19-type effects can affect predictions in our approach and in the classical one. In particular, death rates forecasts tend to be more robust compared to models with a cohort effect, and the regularized model outperforms the so-called P-spline model in terms of prediction and stability. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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18 pages, 1470 KiB

Open AccessArticle

The Linear Link: Deriving Age-Specific Death Rates from Life Expectancy

by Marius D. Pascariu, Ugofilippo Basellini, José Manuel Aburto and Vladimir Canudas-Romo

Risks 2020, 8(4), 109; https://doi.org/10.3390/risks8040109 - 20 Oct 2020

Cited by 9 | Viewed by 5605

Abstract

The prediction of human longevity levels in the future by direct forecasting of life expectancy offers numerous advantages, compared to methods based on extrapolation of age-specific death rates. However, the reconstruction of accurate life tables starting from a given level of life expectancy [...] Read more.

The prediction of human longevity levels in the future by direct forecasting of life expectancy offers numerous advantages, compared to methods based on extrapolation of age-specific death rates. However, the reconstruction of accurate life tables starting from a given level of life expectancy at birth, or any other age, is not straightforward. Model life tables have been extensively used for estimating age patterns of mortality in poor-data countries. We propose a new model inspired by indirect estimation techniques applied in demography, which can be used to estimate full life tables at any point in time, based on a given value of life expectancy at birth. Our model relies on the existing high correlations between levels of life expectancy and death rates across ages. The methods presented in this paper are implemented in a publicly available R package. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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Graphical abstract

27 pages, 2892 KiB

Open AccessArticle

The Impact of Model Uncertainty on Index-Based Longevity Hedging and Measurement of Longevity Basis Risk

by Uditha Balasooriya, Johnny Siu-Hang Li and Jackie Li

Risks 2020, 8(3), 80; https://doi.org/10.3390/risks8030080 - 1 Aug 2020

Cited by 1 | Viewed by 3240

Abstract

We investigate the impact of model uncertainty on hedging longevity risk with index-based derivatives and assessing longevity basis risk, which arises from the mismatch between the hedging instruments and the portfolio being hedged. We apply the bivariate Lee–Carter model, the common factor model, [...] Read more.

We investigate the impact of model uncertainty on hedging longevity risk with index-based derivatives and assessing longevity basis risk, which arises from the mismatch between the hedging instruments and the portfolio being hedged. We apply the bivariate Lee–Carter model, the common factor model, and the M7-M5 model, with separate cohort effects between the two populations, and various time series processes and simulation methods, to build index-based longevity hedges and measure the hedge effectiveness. Based on our modeling and simulations on hypothetical scenarios, the estimated levels of hedge effectiveness are around 50% to 80% for a large pension plan, and the model selection, particularly in dealing with the computed time series, plays a very important role in the estimation. We also experiment with a modified bootstrapping approach to incorporate the uncertainty of model selection into the modeling of longevity basis risk. The hedging results under this approach may approximately be seen as a “weighted” average of those calculated from the different model candidates. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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11 pages, 376 KiB

Open AccessFeature PaperArticle

Retiree Mortality Forecasting: A Partial Age-Range or a Full Age-Range Model?

by Han Lin Shang and Steven Haberman

Risks 2020, 8(3), 69; https://doi.org/10.3390/risks8030069 - 1 Jul 2020

Cited by 4 | Viewed by 2647

Abstract

An essential input of annuity pricing is the future retiree mortality. From observed age-specific mortality data, modeling and forecasting can take place in two routes. On the one hand, we can first truncate the available data to retiree ages and then produce mortality [...] Read more.

An essential input of annuity pricing is the future retiree mortality. From observed age-specific mortality data, modeling and forecasting can take place in two routes. On the one hand, we can first truncate the available data to retiree ages and then produce mortality forecasts based on a partial age-range model. On the other hand, with all available data, we can first apply a full age-range model to produce forecasts and then truncate the mortality forecasts to retiree ages. We investigate the difference in modeling the logarithmic transformation of the central mortality rates between a partial age-range and a full age-range model, using data from mainly developed countries in the Human Mortality Database (2020). By evaluating and comparing the short-term point and interval forecast accuracies, we recommend the first strategy by truncating all available data to retiree ages and then produce mortality forecasts. However, when considering the long-term forecasts, it is unclear which strategy is better since it is more difficult to find a model and parameters that are optimal. This is a disadvantage of using methods based on time-series extrapolation for long-term forecasting. Instead, an expectation approach, in which experts set a future target, could be considered, noting that this method has also had limited success in the past. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

18 pages, 594 KiB

Open AccessFeature PaperArticle

A Two-Population Extension of the Exponential Smoothing State Space Model with a Smoothing Penalisation Scheme

by Yanlin Shi, Sixian Tang and Jackie Li

Risks 2020, 8(3), 67; https://doi.org/10.3390/risks8030067 - 29 Jun 2020

Cited by 1 | Viewed by 2873

Abstract

The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the [...] Read more.

The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the exponential smoothing state space (ETS) model can produce outstanding prediction performance, while it fails to guarantee the consistency across neighbouring ages. Apart from that, single-population models such as the famous Lee-Carter (LC) may produce divergent forecasts between different populations in the long run and thus lack the property of the so-called coherence. This study extends the original ETS model to a two-population version (2-ETS) and imposes a smoothing penalisation scheme to reduce inconsistency of forecasts across adjacent ages. The exponential smoothing parameters in the 2-ETS model are fitted by a Fourier functional form to reduce dimensionality and thus improve estimation efficiency. We evaluate the performance of the proposed model via an empirical study using Australian female and male population data. Our results demonstrate the superiority of the 2-ETS model over the LC and ETS as well as two multi-population methods - the augmented common factor model (LL) and coherent functional data model (CFDM) regarding forecast accuracy and coherence. Full article

(This article belongs to the Special Issue Mortality Forecasting and Applications)

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