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Open AccessEditorial

Special Issue “Ageing Population Risks”

by Pavel V. Shevchenko

Risks 2018, 6(1), 16; https://doi.org/10.3390/risks6010016 - 5 Mar 2018

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(This article belongs to the Special Issue Ageing Population Risks)

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Open AccessArticle

Assessment of Policy Changes to Means-Tested Age Pension Using the Expected Utility Model: Implication for Decisions in Retirement

by Johan G. Andréasson and Pavel V. Shevchenko

Risks 2017, 5(3), 47; https://doi.org/10.3390/risks5030047 - 9 Sep 2017

Cited by 11 | Viewed by 4788

Abstract

Means-tested pension policies are typical for many countries, and the assessment of policy changes is critical for policy makers. In this paper, we consider the Australian means-tested Age Pension. In 2015, two important changes were made to the popular Allocated Pension accounts: the [...] Read more.

Means-tested pension policies are typical for many countries, and the assessment of policy changes is critical for policy makers. In this paper, we consider the Australian means-tested Age Pension. In 2015, two important changes were made to the popular Allocated Pension accounts: the income means-test is now based on deemed income rather than account withdrawals, and the income-test deduction no longer applies. We examine the implications of the new changes in regard to optimal decisions for consumption, investment and housing. We account for regulatory minimum withdrawal rules that are imposed by regulations on Allocated Pension accounts, as well as the 2017 asset-test rebalancing. The policy changes are considered under a utility-maximising life cycle model solved as an optimal stochastic control problem. We find that the new rules decrease the advantages of planning the consumption in relation to the means-test, while risky asset allocation becomes more sensitive to the asset-test. The difference in optimal drawdown between the old and new policy is only noticeable early in retirement until regulatory minimum withdrawal rates are enforced. However, the amount of extra Age Pension received by many households is now significantly higher due to the new deeming income rules, which benefit wealthier households who previously would not have received Age Pension due to the income-test and minimum withdrawals. Full article

(This article belongs to the Special Issue Ageing Population Risks)

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7864 KiB

Open AccessArticle

Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components

by Dorota Toczydlowska, Gareth W. Peters, Man Chung Fung and Pavel V. Shevchenko

Risks 2017, 5(3), 42; https://doi.org/10.3390/risks5030042 - 27 Jul 2017

Cited by 8 | Viewed by 5024

Abstract

In this study we develop a multi-factor extension of the family of Lee-Carter stochastic mortality models. We build upon the time, period and cohort stochastic model structure to extend it to include exogenous observable demographic features that can be used as additional factors [...] Read more.

In this study we develop a multi-factor extension of the family of Lee-Carter stochastic mortality models. We build upon the time, period and cohort stochastic model structure to extend it to include exogenous observable demographic features that can be used as additional factors to improve model fit and forecasting accuracy. We develop a dimension reduction feature extraction framework which (a) employs projection based techniques of dimensionality reduction; in doing this we also develop (b) a robust feature extraction framework that is amenable to different structures of demographic data; (c) we analyse demographic data sets from the patterns of missingness and the impact of such missingness on the feature extraction, and (d) introduce a class of multi-factor stochastic mortality models incorporating time, period, cohort and demographic features, which we develop within a Bayesian state-space estimation framework; finally (e) we develop an efficient combined Markov chain and filtering framework for sampling the posterior and forecasting. We undertake a detailed case study on the Human Mortality Database demographic data from European countries and we use the extracted features to better explain the term structure of mortality in the UK over time for male and female populations when compared to a pure Lee-Carter stochastic mortality model, demonstrating our feature extraction framework and consequent multi-factor mortality model improves both in sample fit and importantly out-off sample mortality forecasts by a non-trivial gain in performance. Full article

(This article belongs to the Special Issue Ageing Population Risks)

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654 KiB

Open AccessFeature PaperArticle

Actuarial Applications and Estimation of Extended CreditRisk+

by Jonas Hirz, Uwe Schmock and Pavel V. Shevchenko

Risks 2017, 5(2), 23; https://doi.org/10.3390/risks5020023 - 31 Mar 2017

Cited by 6 | Viewed by 8515

Abstract

We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We [...] Read more.

We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We then link our proposed model to an extended version of the credit risk model CreditRisk+. This allows exact risk aggregation via an efficient numerically stable Panjer recursion algorithm and provides numerous applications in credit, life insurance and annuity portfolios to derive P&L distributions. Furthermore, the model allows exact (without Monte Carlo simulation error) calculation of risk measures and their sensitivities with respect to model parameters for P&L distributions such as value-at-risk and expected shortfall. Numerous examples, including an application to partial internal models under Solvency II, using Austrian and Australian data are shown. Full article

(This article belongs to the Special Issue Ageing Population Risks)

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497 KiB

Open AccessArticle

Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates

by Yuan Gao and Han Lin Shang

Risks 2017, 5(2), 21; https://doi.org/10.3390/risks5020021 - 25 Mar 2017

Cited by 9 | Viewed by 6967

Abstract

This study considers the forecasting of mortality rates in multiple populations. We propose a model that combines mortality forecasting and functional data analysis (FDA). Under the FDA framework, the mortality curve of each year is assumed to be a smooth function of age. [...] Read more.

This study considers the forecasting of mortality rates in multiple populations. We propose a model that combines mortality forecasting and functional data analysis (FDA). Under the FDA framework, the mortality curve of each year is assumed to be a smooth function of age. As with most of the functional time series forecasting models, we rely on functional principal component analysis (FPCA) for dimension reduction and further choose a vector error correction model (VECM) to jointly forecast mortality rates in multiple populations. This model incorporates the merits of existing models in that it excludes some of the inherent randomness with the nonparametric smoothing from FDA, and also utilizes the correlation structures between the populations with the use of VECM in mortality models. A nonparametric bootstrap method is also introduced to construct interval forecasts. The usefulness of this model is demonstrated through a series of simulation studies and applications to the age-and sex-specific mortality rates in Switzerland and the Czech Republic. The point forecast errors of several forecasting methods are compared and interval scores are used to evaluate and compare the interval forecasts. Our model provides improved forecast accuracy in most cases. Full article

(This article belongs to the Special Issue Ageing Population Risks)

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455 KiB

Open AccessArticle

Optimal Time to Enter a Retirement Village

by Jinhui Zhang, Sachi Purcal and Jiaqin Wei

Risks 2017, 5(1), 20; https://doi.org/10.3390/risks5010020 - 22 Mar 2017

Cited by 3 | Viewed by 4568

Abstract

We consider the financial planning problem of a retiree wishing to enter a retirement village at a future uncertain date. The date of entry is determined by the retiree’s utility and bequest maximisation problem within the context of uncertain future health states. In [...] Read more.

We consider the financial planning problem of a retiree wishing to enter a retirement village at a future uncertain date. The date of entry is determined by the retiree’s utility and bequest maximisation problem within the context of uncertain future health states. In addition, the retiree must choose optimal consumption, investment, bequest and purchase of insurance products prior to their full annuitisation on entry to the retirement village. A hyperbolic absolute risk-aversion (HARA) utility function is used to allow necessary consumption for basic living and medical costs. The retirement village will typically require an initial deposit upon entry. This threshold wealth requirement leads to exercising the replication of an American put option at the uncertain stopping time. From our numerical results, active insurance and annuity markets are shown to be a critical aspect in retirement planning. Full article

(This article belongs to the Special Issue Ageing Population Risks)

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746 KiB

Open AccessArticle

Evaluating Extensions to Coherent Mortality Forecasting Models

by Syazreen Shair, Sachi Purcal and Nick Parr

Risks 2017, 5(1), 16; https://doi.org/10.3390/risks5010016 - 10 Mar 2017

Cited by 14 | Viewed by 5167

Abstract

Coherent models were developed recently to forecast the mortality of two or more sub-populations simultaneously and to ensure long-term non-divergent mortality forecasts of sub-populations. This paper evaluates the forecast accuracy of two recently-published coherent mortality models, the Poisson common factor and the product-ratio [...] Read more.

Coherent models were developed recently to forecast the mortality of two or more sub-populations simultaneously and to ensure long-term non-divergent mortality forecasts of sub-populations. This paper evaluates the forecast accuracy of two recently-published coherent mortality models, the Poisson common factor and the product-ratio functional models. These models are compared to each other and the corresponding independent models, as well as the original Lee–Carter model. All models are applied to age-gender-speciﬁc mortality data for Australia and Malaysia and age-gender-ethnicity-speciﬁc data for Malaysia. The out-of-sample forecast error of log death rates, male-to-female death rate ratios and life expectancy at birth from each model are compared and examined across groups. The results show that, in terms of overall accuracy, the forecasts of both coherent models are consistently more accurate than those of the independent models for Australia and for Malaysia, but the relative performance differs by forecast horizon. Although the product-ratio functional model outperforms the Poisson common factor model for Australia, the Poisson common factor is more accurate for Malaysia. For the ethnic groups application, ethnic-coherence gives better results than gender-coherence. The results provide evidence that coherent models are preferable to independent models for forecasting sub-populations’ mortality. Full article

(This article belongs to the Special Issue Ageing Population Risks)

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2740 KiB

Open AccessFeature PaperArticle

Incorporation of Stochastic Policyholder Behavior in Analytical Pricing of GMABs and GMDBs

by Marcos Escobar, Mikhail Krayzler, Franz Ramsauer, David Saunders and Rudi Zagst

Risks 2016, 4(4), 41; https://doi.org/10.3390/risks4040041 - 8 Nov 2016

Cited by 13 | Viewed by 5645

Abstract

Variable annuities represent certain unit-linked life insurance products offering different types of protection commonly referred to as guaranteed minimum benefits (GMXBs). They are designed for the increasing demand of the customers for private pension provision. In this paper we analytically price variable annuities [...] Read more.

Variable annuities represent certain unit-linked life insurance products offering different types of protection commonly referred to as guaranteed minimum benefits (GMXBs). They are designed for the increasing demand of the customers for private pension provision. In this paper we analytically price variable annuities with guaranteed minimum repayments at maturity and in case of the insured’s death. If the contract is prematurely surrendered, the policyholder is entitled to the current value of the fund account reduced by the prevailing surrender fee. The financial market and the mortality model are affine linear. For the surrender model, a Cox process is deployed whose intensity is given by a deterministic function (s-curve) with stochastic inputs from the financial market. So, the policyholders’ surrender behavior depends on the performance of the financial market and is stochastic. The presented pricing scheme incorporates the stochastic surrender behavior of the policyholders and is only based on suitable closed-form approximations. Full article

(This article belongs to the Special Issue Ageing Population Risks)

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