Journal articles: 'Longevity and mortality risk'

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Yue, Jack C. "Mortality Compression and Longevity Risk." North American Actuarial Journal 16, no. 4 (October 2012): 434–48. http://dx.doi.org/10.1080/10920277.2012.10597641.

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Blake, D., A. J. G. Cairns, and K. Dowd. "Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities." British Actuarial Journal 12, no. 1 (March 1, 2006): 153–97. http://dx.doi.org/10.1017/s1357321700004736.

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ABSTRACTThis paper addresses the problem of longevity risk — the risk of uncertain aggregate mortality — and discusses the ways in which life assurers, annuity providers and pension plans can manage their exposure to this risk. In particular, it focuses on how they can use mortality-linked securities and over-the-counter contracts — some existing and others still hypothetical — to manage their longevity risk exposures. It provides a detailed analysis of two such securities — the Swiss Re mortality bond issued in December 2003 and the EIB/BNP longevity bond announced in November 2004. It then looks at the universe of hypothetical mortality-linked securities — other forms of longevity bonds, swaps, futures and options — and investigates their potential uses. It also addresses implementation issues, and draws lessons from the experiences of other derivative contracts. Particular attention is paid to the issues involved with the construction and use of mortality indices, the management of the associated credit risks, and possible barriers to the development of markets for these securities. It suggests that these implementation difficulties are essentially teething problems that will be resolved over time, and so leave the way open to the development of flourishing markets in a brand new class of securities.

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Woo, G., C. J. Martin, C. Hornsby, and A. W. Coburn. "Prospective Longevity Risk Analysis." British Actuarial Journal 15, S1 (2009): 235–47. http://dx.doi.org/10.1017/s1357321700005584.

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ABSTRACTMortality improvement has traditionally been analysed using an array of statistical methods, and extrapolated to make actuarial projections. This paper presents a forward-looking approach to longevity risk analysis which is based on stochastic modelling of the underlying causes of mortality improvement, due to changes in lifestyle, health environment, and advances in medical science. The rationale for this approach is similar to that adopted for modelling other types of dynamic insurance risk, e.g. natural catastrophes, where risk analysts construct a stochastic ensemble of events that might happen in the future, rather than rely on a retrospective analysis of the non-stationary and comparatively brief historical record.Another feature of prospective longevity risk analysis, which is shared with catastrophe risk modelling, is the objective of capturing vulnerability data at a high resolution, to maximise the benefit of detailed modelling capability down to individual risk factor level. Already, the use by insurers of postcode data for U.K. flood risk assessment has carried over to U.K. mortality assessment. Powered by fast numerical computation and parameterised with high quality geographical data, hydrological models of flood risk have superseded the traditional statistical insurance loss models. A decade later, medically-motivated computational models of mortality risk can be expected to gain increasing prominence in longevity risk management.

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Levantesi, Susanna, Andrea Nigri, and Gabriella Piscopo. "Longevity risk management through Machine Learning: state of the art." Insurance Markets and Companies 11, no. 1 (November 25, 2020): 11–20. http://dx.doi.org/10.21511/ins.11(1).2020.02.

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Longevity risk management is an area of the life insurance business where the use of Artificial Intelligence is still underdeveloped. The paper retraces the main results of the recent actuarial literature on the topic to draw attention to the potential of Machine Learning in predicting mortality and consequently improving the longevity risk quantification and management, with practical implication on the pricing of life products with long-term duration and lifelong guaranteed options embedded in pension contracts or health insurance products. The application of AI methodologies to mortality forecasts improves both fitting and forecasting of the models traditionally used. In particular, the paper presents the Classification and the Regression Tree framework and the Neural Network algorithm applied to mortality data. The literature results are discussed, focusing on the forecasting performance of the Machine Learning techniques concerning the classical model. Finally, a reflection on both the great potentials of using Machine Learning in longevity management and its drawbacks is offered.

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Lin, Tzuling, and Cary Chi-Liang Tsai. "On the mortality/longevity risk hedging with mortality immunization." Insurance: Mathematics and Economics 53, no. 3 (November 2013): 580–96. http://dx.doi.org/10.1016/j.insmatheco.2013.08.006.

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Deng, Yinglu, Patrick L. Brockett, and Richard D. MacMinn. "Longevity/Mortality Risk Modeling and Securities Pricing." Journal of Risk and Insurance 79, no. 3 (February 8, 2012): 697–721. http://dx.doi.org/10.1111/j.1539-6975.2011.01450.x.

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Wingenbach, Rachel, Jong-Min Kim, and Hojin Jung. "Living longer in high longevity risk." Journal of Demographic Economics 86, no. 1 (February 7, 2020): 47–86. http://dx.doi.org/10.1017/dem.2019.20.

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AbstractThere is considerable uncertainty regarding changes in future mortality rates. This article investigates the impact of such longevity risk on discounted government annuity benefits for retirees. It is critical to forecast more accurate future mortality rates to improve our estimation of an expected annuity payout. Thus, we utilize the Lee–Carter model, which is well-known as a parsimonious dynamic mortality model. We find strong evidence that female retirees are likely to receive more public lifetime annuity than males in the USA, which is associated with systematic mortality rate differences between genders. A cross-country comparison presents that the current public annuity system would not fully cover retiree's longevity risk. Every additional year of life expectancy leaves future retirees exposed to high risk, arising from high volatility of lifetime annuities. Also, because the growth in life expectancy is higher than the growth of expected public pension, there will be a financial risk to retirees.

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Choulli, Tahir, Catherine Daveloose, and Michèle Vanmaele. "Mortality/Longevity Risk-Minimization with or without Securitization." Mathematics 9, no. 14 (July 10, 2021): 1629. http://dx.doi.org/10.3390/math9141629.

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This paper addresses the risk-minimization problem, with and without mortality securitization, à la Föllmer–Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework includes situations in which the correlation between the market model and the time of death is arbitrary general, and hence leads to the case of a market model where there are two levels of information—the public information, which is generated by the financial assets, and a larger flow of information that contains additional knowledge about the death time of an insured. By enlarging the filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction. Our key tool lies in our optional martingale representation, which states that any martingale in the large filtration stopped at the death time can be decomposed into precise orthogonal local martingales. This allows us to derive the dynamics of the value processes of the mortality/longevity securities used for the securitization, and to decompose any mortality/longevity liability into the sum of orthogonal risks by means of a risk basis. The first main contribution of this paper resides in quantifying, as explicitly as possible, the effect of mortality on the risk-minimizing strategy by determining the optimal strategy in the enlarged filtration in terms of strategies in the smaller filtration. Our second main contribution consists of finding risk-minimizing strategies with insurance securitization by investing in stocks and one (or more) mortality/longevity derivatives such as longevity bonds. This generalizes the existing literature on risk-minimization using mortality securitization in many directions.

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Fung, Man Chung, Katja Ignatieva, and Michael Sherris. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives." Risks 7, no. 1 (January 3, 2019): 2. http://dx.doi.org/10.3390/risks7010002.

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This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of longevity derivatives are derived. The model is calibrated using Australian mortality data. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the longevity risk premium, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The results compare the risk management benefits and costs of longevity derivatives with linear and nonlinear payoff structures.

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Hanewald, Katja, John Piggott, and Michael Sherris. "Individual post-retirement longevity risk management under systematic mortality risk." Insurance: Mathematics and Economics 52, no. 1 (January 2013): 87–97. http://dx.doi.org/10.1016/j.insmatheco.2012.11.002.

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Wang, Hsin-Chung, Ching-Syang Jack Yue, and Chen-Tai Chong. "Mortality models and longevity risk for small populations." Insurance: Mathematics and Economics 78 (January 2018): 351–59. http://dx.doi.org/10.1016/j.insmatheco.2017.09.020.

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Chuliá, Helena, Montserrat Guillén, and Jorge M. Uribe. "MODELING LONGEVITY RISK WITH GENERALIZED DYNAMIC FACTOR MODELS AND VINE-COPULAE." ASTIN Bulletin 46, no. 1 (November 11, 2015): 165–90. http://dx.doi.org/10.1017/asb.2015.21.

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AbstractWe present a methodology to forecast mortality rates and estimate longevity and mortality risks. The methodology uses generalized dynamic factor models fitted to the differences in the log-mortality rates. We compare their prediction performance with that of models previously described in the literature, including the traditional static factor model fitted to log-mortality rates. We also construct risk measures using vine-copula simulations, which take into account the dependence between the idiosyncratic components of the mortality rates. The methodology is applied to forecast mortality rates for a population portfolio for the UK and to estimate longevity and mortality risks.

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Wong, Tat Wing, Mei Choi Chiu, and Hoi Ying Wong. "Managing Mortality Risk With Longevity Bonds When Mortality Rates Are Cointegrated." Journal of Risk and Insurance 84, no. 3 (October 23, 2015): 987–1023. http://dx.doi.org/10.1111/jori.12110.

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Zhang, Ning. "The Modified Mortality Decomposition Model and its Application in the China Longevity Risk Analysis." Advanced Materials Research 756-759 (September 2013): 2912–17. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.2912.

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the paper made an adjustment on the mortality decomposition model which was first proposed by the author. The mortality data can be processed by the classical wavelet and HHT methods. Compared with the classical mortality analyzing method, more information about longevity risk can be captured by the adjusted mortality decomposition. As a new development, the adjusted mortality decomposition is more effective for the short data set like China. Also the paper gave a modified form of longevity risk index which is different from that the author introduced in another paper. The new modified index is more suitable for China. Based on the adjusted decomposition of mortality rate data and modified longevity risk index, the paper gave their application and detailed analysis on China longevity risk. The important result of different provinces is also given.

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Dzingirai, Canicio, and Nixon S. Chekenya. "Longevity swaps for longevity risk management in life insurance products." Journal of Risk Finance 21, no. 3 (June 27, 2020): 253–69. http://dx.doi.org/10.1108/jrf-05-2019-0085.

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Purpose The life insurance industry has been exposed to high levels of longevity risk born from the mismatch between realized mortality trends and anticipated forecast. Annuity providers are exposed to extended periods of annuity payments. There are no immediate instruments in the market to counter the risk directly. This paper aims to develop appropriate instruments for hedging longevity risk and providing an insight on how existing products can be tailor-made to effectively immunize portfolios consisting of life insurance using a cointegration vector error correction model with regime-switching (RS-VECM), which enables both short-term fluctuations, through the autoregressive structure [AR(1)] and long-run equilibria using a cointegration relationship. The authors also develop synthetic products that can be used to effectively hedge longevity risk faced by life insurance and annuity providers who actively hold portfolios of life insurance products. Models are derived using South African data. The authors also derive closed-form expressions for hedge ratios associated with synthetic products written on life insurance contracts as this will provide a natural way of immunizing the associated portfolios. The authors further show how to address the current liquidity challenges in the longevity market by devising longevity swaps and develop pricing and hedging algorithms for longevity-linked securities. The use of a cointergrating relationship improves the model fitting process, as all the VECMs and RS-VECMs yield greater criteria values than their vector autoregressive model (VAR) and regime-switching vector autoregressive model (RS-VAR) counterpart’s, even though there are accruing parameters involved. Design/methodology/approach The market model adopted from Ngai and Sherris (2011) is a cointegration RS-VECM for this enables both short-term fluctuations, through the AR(1) and long-run equilibria using a cointegration relationship (Johansen, 1988, 1995a, 1995b), with a heteroskedasticity through the use of regime-switching. The RS-VECM is seen to have the best fit for Australian data under various model selection criteria by Sherris and Zhang (2009). Harris (1997) (Sajjad et al., 2008) also fits a regime-switching VAR model using Australian (UK and US) data to four key macroeconomic variables (market stock indices), showing that regime-switching is a significant improvement over autoregressive conditional heteroscedasticity (ARCH) and generalised autoregressive conditional heteroscedasticity (GARCH) processes in the account for volatility, evidence similar to that of Sherris and Zhang (2009) in the case of Exponential Regressive Conditional Heteroscedasticity (ERCH). Ngai and Sherris (2011) and Sherris and Zhang (2009) also fit a VAR model to Australian data with simultaneous regime-switching across many economic and financial series. Findings The authors develop a longevity swap using nighttime data instead of usual income measures as it yields statistically accurate results. The authors also develop longevity derivatives and annuities including variable annuities with guaranteed lifetime withdrawal benefit (GLWB) and inflation-indexed annuities. Improved market and mortality models are developed and estimated using South African data to model the underlying risks. Macroeconomic variables dependence is modeled using a cointegrating VECM as used in Ngai and Sherris (2011), which enables both short-run dependence and long-run equilibrium. Longevity swaps provide protection against longevity risk and benefit the most from hedging longevity risk. Longevity bonds are also effective as a hedging instrument in life annuities. The cost of hedging, as reflected in the price of longevity risk, has a statistically significant effect on the effectiveness of hedging options. Research limitations/implications This study relied on secondary data partly reported by independent institutions and the government, which may be biased because of smoothening, interpolation or extrapolation processes. Practical implications An examination of South Africa’s mortality based on industry experience in comparison to population mortality would demand confirmation of the analysis in this paper based on Belgian data as well as other less developed economies. This study shows that to provide inflation-indexed life annuities, there is a need for an active market for hedging inflation in South Africa. This would demand the South African Government through the help of Actuarial Society of South Africa (ASSA) to issue inflation-indexed securities which will help annuities and insurance providers immunize their portfolios from longevity risk. Social implications In South Africa, there is an infant market for inflation hedging and no market for longevity swaps. The effect of not being able to hedge inflation is guaranteed, and longevity swaps in annuity products is revealed to be useful and significant, particularly using developing or emerging economies as a laboratory. This study has shown that government issuance or allowing issuance, of longevity swaps, can enable insurers to manage longevity risk. If the South African Government, through ASSA, is to develop a projected mortality reference index for South Africa, this would allow the development of mortality-linked securities and longevity swaps which ultimately maximize the social welfare of life assurance policy holders. Originality/value The paper proposes longevity swaps and static hedging because they are simple, less costly and practical with feasible applications to the South African market, an economy of over 50 million people. As the market for MLS develops further, dynamic hedging should become possible.

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Zhao, Ming, Ziwen Li, Yinge Cai, and Weiting Li. "Measurement of Longevity Risk of Life Annuity Based on C-ROSS Framework." Mathematical Problems in Engineering 2020 (September 18, 2020): 1–8. http://dx.doi.org/10.1155/2020/1746413.

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This paper constructs a model to measure longevity risk and explains the reasons for restricting the supply of annuity products in life insurance companies. According to the Lee–Carter Model and the VaR-based stochastic simulation, it can be found that the risk margin of the first type of longevity risk for ignoring the improvement of mortality rate is about 7%, and the risk margin of the second type of longevity risk for underestimating mortality improvement is about 7%. Therefore, the insurer needs to use cohort life table pricing premium and gradually prepares longevity risk capital during the insurance period.

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Börger, Matthias, Daniel Fleischer, and Nikita Kuksin. "MODELING THE MORTALITY TREND UNDER MODERN SOLVENCY REGIMES." ASTIN Bulletin 44, no. 1 (October 10, 2013): 1–38. http://dx.doi.org/10.1017/asb.2013.24.

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AbstractStochastic modeling of mortality/longevity risks is necessary for internal models of (re)insurers under the new solvency regimes, such as Solvency II and the Swiss Solvency Test. In this paper, we propose a mortality model which fulfills all requirements imposed by these regimes. We show how the model can be calibrated and applied to the simultaneous modeling of both mortality and longevity risk for several populations. The main contribution of this paper is a stochastic trend component which explicitly models changes in the long-term mortality trend assumption over time. This allows to quantify mortality and longevity risk over the one-year time horizon prescribed by the solvency regimes without relying on nested simulations. We illustrate the practical ability of our model by calculating solvency capital requirements for some example portfolios, and we compare these capital requirements with those from the Solvency II standard formula.

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Richter, Andreas, and Frederik Weber. "Mortality-Indexed Annuities Managing Longevity Risk Via Product Design." North American Actuarial Journal 15, no. 2 (April 2011): 212–36. http://dx.doi.org/10.1080/10920277.2011.10597618.

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Plat, Richard. "One-year Value-at-Risk for longevity and mortality." Insurance: Mathematics and Economics 49, no. 3 (November 2011): 462–70. http://dx.doi.org/10.1016/j.insmatheco.2011.07.002.

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Blackburn, Craig, and Michael Sherris. "Consistent dynamic affine mortality models for longevity risk applications." Insurance: Mathematics and Economics 53, no. 1 (July 2013): 64–73. http://dx.doi.org/10.1016/j.insmatheco.2013.04.007.

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Kamilar, Jason M., Richard G. Bribiescas, and Brenda J. Bradley. "Is group size related to longevity in mammals?" Biology Letters 6, no. 6 (May 12, 2010): 736–39. http://dx.doi.org/10.1098/rsbl.2010.0348.

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Life-history theory predicts that reduced extrinsic risk of mortality should increase species longevity over evolutionary time. Increasing group size should reduce an individual's risk of predation, and consequently reduce its extrinsic risk of mortality. Therefore, we should expect a relationship between group size and maximum longevity across species, while controlling for well-known correlates of longevity. We tested this hypothesis using a dataset of 253 mammal species and phylogenetic comparative methods. We found that group size was a poor predictor of maximum longevity across all mammals, as well as within primates and rodents. We found a weak but significant group-size effect on artiodactyl longevity, but in a negative direction. Body mass was consistently the best predictor of maximum longevity, which may be owing to lower predation risk and/or lower basal metabolic rates for large species. Artiodactyls living in large groups may exhibit higher rates of extrinsic mortality because of being more conspicuous to predators in open habitats, resulting in shorter lifespans.

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Zou, Xiaopeng, Zihan Ye, and Qiuzi Zhang. "Securitization of longevity risk – survivor swap perspective." China Finance Review International 6, no. 4 (November 21, 2016): 322–41. http://dx.doi.org/10.1108/cfri-06-2015-0092.

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Purpose The purpose of this paper is to present a clear path to securitize the longevity risk with two distinct swaps in order to inspire a new Chinese life market. Design/methodology/approach Studies on longevity risk securitization consist of three aspects, respectively, instrument design, pricing methodology and mortality projection. The swaps designed are referenced, respectively, to vanilla and complex survivor swaps (Dowd et al., 2006; Lin and Cox, 2005). Methods applied are RHH model and Gompertz law for mortality projection, as well as two-factor Wang transformation for pricing. Findings This paper figures out the market price of risk in Chinese annuity market, checks for the sensitivity of the price to parameters and tests the hedging effects by Monte Carlo simulation. Originality/value Based on the theoretical and numerical results, this paper suggests an effective way to possibly witness the birth of New Life Market in China.

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Gemmo, Irina, Ralph Rogalla, and Jan-Hendrik Weinert. "Optimal portfolio choice with tontines under systematic longevity risk." Annals of Actuarial Science 14, no. 2 (July 13, 2020): 302–15. http://dx.doi.org/10.1017/s1748499520000214.

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AbstractWe derive optimal portfolio choice patterns in retirement (ages 66–105) for a constant relative risk aversion utility maximising investor facing risky capital market returns, stochastic mortality risk, and income-reducing health shocks. Beyond the usual stocks and bonds, the individual can invest his assets in tontines. Tontines are cost-efficient financial contracts providing age-increasing, but volatile cash flows, generated through the pooling of mortality without guarantees, which can help to match increasing financing needs at old ages. We find that a tontine invested in the risk-free asset dominates stock investments for older investors without a bequest motive. However, with a bequest motive, it is optimal to replace the tontine investment over time with traditional financial assets. Our results indicate that early in retirement, a tontine is only an attractive investment option, if the tontine funds are invested in a risky asset. In this case, they crowd out stocks and risk-free bonds in the optimal portfolios of younger investors. Over time, the average optimal portfolio weight of tontines decreases. Introducing systematic mortality risks noticeably reduces the peak allocation to tontines.

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Lu, Jiehua, and Hui Zhu. "An Empirical Analysis of the Determinants of Mortality Risks of Chinese Centenarians in the Era of Longevity." Innovation in Aging 4, Supplement_1 (December 1, 2020): 340. http://dx.doi.org/10.1093/geroni/igaa057.1091.

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Abstract With the rapid socioeconomic development and the increasing average life expectancy, China has shifted into an era of longevity. One significant feature of this era is the increasing size of Chinese centenarians and their health status are attracting increasing attention from academic communities. By using Chinese Longitudinal Healthy Longevity Survey (CLHLS), this paper employs Cox model to pinpoint the key influencing factors of mortality risk of Chinese centenarians. Our findings turn out that compared with the other elderly population, the mortality-risk determinants among centenarians are unique. The most important risk of the latter comes from their objective health status. The worse the health situation, the higher mortality risk is. Meanwhile, this rate is less affected by social and economic conditions. However, gender and smoking habit all play parts in the mortality risk of centenarians. This study comprehensively understands the key factors of the mortality risk of Chinese centenarians, which is of great significance for reducing centenarians’ mortality risks and enhancing their health and well-beings.

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Šiškina, Natalja, and Jonas Šiaulys. "ARMA Models for Mortality Forecast." Lietuvos statistikos darbai 55, no. 1 (December 20, 2016): 31–44. http://dx.doi.org/10.15388/ljs.2016.13865.

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In the last several decades, many countries have been paying a lot of attention to mortality forecastingbecause of high longevity risk. The purpose of this paper is to analyze mortality characteristics of Baltic countries andmake predictions using ARMA models. Research shoved that mortality rate distribution is almost the same in Lithuania, Latvia and Estonia and all of them represent longevity trends. It means that men and women, children and adults have thesame mortality structure in all Baltic countries and live longer than before.

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Özen, Selin, and Şule Şahin. "A Two-Population Mortality Model to Assess Longevity Basis Risk." Risks 9, no. 2 (February 20, 2021): 44. http://dx.doi.org/10.3390/risks9020044.

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Index-based hedging solutions are used to transfer the longevity risk to the capital markets. However, mismatches between the liability of the hedger and the hedging instrument cause longevity basis risk. Therefore, an appropriate two-population model to measure and assess longevity basis risk is required. In this paper, we aim to construct a two-population mortality model to provide an effective hedge against the basis risk. The reference population is modelled by using the Lee–Carter model with the renewal process and exponential jumps, and the dynamics of the book population are specified. The analysis based on the U.K. mortality data indicate that the proposed model for the reference population and the common age effect model for the book population provide a better fit compared to the other models considered in the paper. Different two-population models are used to investigate the impact of sampling risk on the index-based hedge, as well as to analyse the risk reduction regarding hedge effectiveness. The results show that the proposed model provides a significant risk reduction when mortality jumps and sampling risk are taken into account.

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Kling, Alexander, Jochen Ruß, and Katja Schilling. "RISK ANALYSIS OF ANNUITY CONVERSION OPTIONS IN A STOCHASTIC MORTALITY ENVIRONMENT." ASTIN Bulletin 44, no. 2 (April 9, 2014): 197–236. http://dx.doi.org/10.1017/asb.2014.7.

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AbstractWhile extensive literature exists on the valuation and risk management of financial guarantees embedded in insurance contracts, both the corresponding longevity guarantees and interactions between financial and longevity guarantees are often ignored. The present paper provides a framework for a joint analysis of financial and longevity guarantees, and applies this framework to different annuity conversion options in deferred unit-linked annuities. In particular, we analyze and compare different versions of so-called guaranteed annuity options and guaranteed minimum income benefits with respect to the value of the option and the resulting risk for the insurer. Furthermore, we examine whether and to what extent an insurance company is able to reduce the risk by typical risk management strategies. The analysis is based on a combined stochastic model for both financial market and future survival probabilities. We show that different annuity conversion options have significantly different option values, and that different risk management strategies lead to a significantly different risk for the insurance company.

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Ng, Reuben, Heather G. Allore, and Becca R. Levy. "Self-Acceptance and Interdependence Promote Longevity: Evidence From a 20-year Prospective Cohort Study." International Journal of Environmental Research and Public Health 17, no. 16 (August 18, 2020): 5980. http://dx.doi.org/10.3390/ijerph17165980.

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We explored psychosocial pathways to longevity, specifically, the association between psychological well-being and mortality in a 20-year prospective cohort study of 7626 participants. As hypothesized, high self-acceptance and interdependence were associated with decreased mortality risk, controlling for other psychological components (purpose, positive relations, growth, mastery) and potential confounders: personality, depression, self-rated health, smoking status, body mass index (BMI), illness, and demographics. Self-acceptance decreased mortality risk by 19% and added three years of life. Longevity expectation fully mediated the relationship between self-acceptance and mortality. Interdependence decreased mortality risk by 17% and added two years of life. Serenity towards death fully mediated the relationship between interdependence and mortality. This is the first known study to investigate self-acceptance, interdependence, and serenity toward death as promoters of longevity, and distilled the relative contributions of these factors, controlling for covariates—all of which were measured over multiple time points. Theoretically, this study suggests that components of well-being may make meaningful contributions to longevity, and practically recommend that self-acceptance and interdependence could be added to interventions to promote aging health.

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D’Amato, Valeria, Mariarosaria Coppola, Susanna Levantesi, Massimiliano Menzietti, and Maria Russolillo. "A longevity basis risk analysis in a joint FDM framework." Journal of Risk Finance 18, no. 1 (January 16, 2017): 55–75. http://dx.doi.org/10.1108/jrf-03-2016-0030.

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Purpose The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless, the difference between the reference population of the hedging instrument and the population of members of a pension plan, or the beneficiaries of an annuity portfolio, determines a significant heterogeneity causing the so-called basis risk. In particular, it is shown that if insurers use financial instruments based on national indices to hedge longevity risk, this hedge can become imperfect. For this reason, it is fundamental to arrange a model allowing to quantify the basis risk for minimising it through a correct calibration of the hedging instrument. Design/methodology/approach The paper provides a framework for measuring the basis risk impact on the. To this aim, we propose a model that measures the population basis risk involved in a longevity hedge, in the functional data model setting. hedging strategies. Findings The innovative contribution of the paper occurs in two key points: the modelling of mortality and the hedging strategy. Regarding the first point, the paper proposes a functional demographic model framework (FDMF) for capturing the basis risk. The FDMF model generally designed for single population combines functional data analysis, nonparametric smoothing and robust statistics. It allows to capture the variability of the mortality trend, by separating out the effects of several orthogonal components. The novelty is to set the FDMF for modelling the mortality of the two populations, the hedging and the exposed one. Regarding the second point, the basic idea is to calibrate the hedging strategy determining a suitable mixture of q-forwards linked to mortality rates to maximise the degree of longevity risk reduction. This calibration is based on the key q-duration intended as a measure allowing to estimate the price sensitivity of the annuity portfolio to the changes in the underlying mortality curve. Originality/value The novelty lies in linking the shift in the mortality curve to the standard deviation of the historical mortality rates of the exposed population. This choice has been determined by the observation that the shock in a mortality rate is age dependent. The main advantage of the presented framework is its strong versatility, being the functional demographic setting a generalisation of the Lee-Carter model commonly used in mortality forecasting, it allows to adapt to different demographic scenarios. In the next developments, we set out to compare other common factor models to assess the most effective longevity hedge. Moreover, the parsimony for considering together two trajectories of the populations under consideration and the convergence of long-term forecast are important aspects of our approach.

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Freimann, Arne. "PRICING LONGEVITY-LINKED SECURITIES IN THE PRESENCE OF MORTALITY TREND CHANGES." ASTIN Bulletin 51, no. 2 (March 10, 2021): 411–47. http://dx.doi.org/10.1017/asb.2021.5.

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ABSTRACTEven though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.

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조재훈 and 이강수. "A stochastic mortality model for annuities to calibrate longevity risk." Journal of Risk Management 29, no. 1 (March 2018): 1–32. http://dx.doi.org/10.21480/tjrm.29.1.201803.001.

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Li, Johnny Siu-Hang, Wai-Sum Chan, and Rui Zhou. "Semicoherent Multipopulation Mortality Modeling: The Impact on Longevity Risk Securitization." Journal of Risk and Insurance 84, no. 3 (September 4, 2016): 1025–65. http://dx.doi.org/10.1111/jori.12135.

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Lemoine, Killian. "Mortality regimes and longevity risk in a life annuity portfolio." Scandinavian Actuarial Journal 2015, no. 8 (February 11, 2014): 689–724. http://dx.doi.org/10.1080/03461238.2014.882860.

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Boonen, Tim J., Anja De Waegenaere, and Henk Norde. "Redistribution of longevity risk: The effect of heterogeneous mortality beliefs." Insurance: Mathematics and Economics 72 (January 2017): 175–88. http://dx.doi.org/10.1016/j.insmatheco.2016.11.004.

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Kuh, D., R. Hardy, M. Hotopf, D. A. Lawlor, B. Maughan, R. Westendorp, R. Cooper, S. Black, and G. D. Mishra. "A Review of Lifetime Risk Factors for Mortality." British Actuarial Journal 15, S1 (2009): 17–64. http://dx.doi.org/10.1017/s135732170000550x.

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ABSTRACTThis review was undertaken for the Faculty and Institute of Actuaries as part of their programme to encourage research collaborations between health researchers and actuaries in order to understand better the factors influencing mortality and longevity. The authors presented their findings in a number of linked sessions at the Edinburgh conference (Joining Forces on Mortality and Longevity) in October 2009 and contributed to this overview. The purpose is to review evidence for the impact on adult mortality of characteristics of the individual's lifetime socioeconomic or psychosocial environment or phenotype at the behavioural; multi-system (e.g. cognitive and physical function); or body system level (e.g. vascular and metabolic traits) that may be common risk factors for a number of major causes of death. This review shows there is growing evidence from large studies and systematic reviews that these individual characteristics, measured in pre-adult as well as the adult life, are associated with later mortality risk. The relative contribution of lifetime environment, genetic factors and chance, whether these contributions change with age, and the underlying social and biological pathways are still to be clarified. This review identifies areas where further life course research is warranted.

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KREMER, ALEXANDER, FRIEDRICH LIESE, SUSANNE HOMÖLLE, and JOHANN CLAUSEN. "Optimal consumption and portfolio choice of retirees with longevity risk." Journal of Pension Economics and Finance 13, no. 3 (October 10, 2013): 227–49. http://dx.doi.org/10.1017/s1474747213000280.

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AbstractThe question how to optimize consumption and portfolio choice over the life cycle has been widely discussed in the literature so far. In this paper we concentrate on a retiree's optimal consumption and portfolio selection over his remaining years of life. We apply the logistic model of mortality thus modeling the empirically observed increase of mortality during the retirement period. The optimal consumption strategy and portfolio choice are established by reducing the Hamilton-Jacobi-Bellmann equation to the explicit solution of an ordinary differential function (ODF) that includes the mortality rate. A general finding is that the Merton-Samuelson result of constant portfolio choice for a constant mortality is confirmed for arbitrary mortality. The portfolio choice is only influenced by risk and return of assets and the retirees’ risk aversion. To get the specific optimal consumption strategy in a realistic situation the logistic model of mortality has been fitted to the data of the Statistical Yearbook for the Federal Republic of Germany 2006/2008. The optimal initial value for the ODF is obtained by numerical methods. The solution provides a large increase in the ratio of optimal consumption to wealth up to about 92 years followed by a sharp decrease. A bequest motive dampens the magnitudes of the ups and downs of the consumption ratio but does not change the basic shape.

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TEMBY, OWEN F., and KEN R. SMITH. "THE ASSOCIATION BETWEEN ADULT MORTALITY RISK AND FAMILY HISTORY OF LONGEVITY: THE MODERATING EFFECTS OF SOCIOECONOMIC STATUS." Journal of Biosocial Science 46, no. 6 (October 8, 2013): 703–16. http://dx.doi.org/10.1017/s0021932013000515.

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SummaryStudies consistently show that increasing levels of socioeconomic status (SES) and having a familial history of longevity reduce the risk of mortality. But do these two variables interact, such that individuals with lower levels of SES, for example, may experience an attenuated longevity penalty by virtue of having long-lived relatives? This article examines this interaction by analysing survival past age 40 based on data from the Utah Population Database on an extinct cohort of men born from the years 1840 to 1909. Cox proportional hazards regression and logistic regression are used to test for the main and interaction mortality effects of SES and familial excess longevity (FEL), a summary measure of an individual's history of longevity among his or her relatives. This research finds that the mortality hazard rate for men in the top 15th percentile of occupational status decreases more as FEL increases than it does among men in the bottom 15th percentile. In addition, the mortality hazard rate among farmers decreases more as FEL increases than it does for non-farmers. With a strong family history of longevity as a proxy for a genetic predisposition, this research suggests that a gene–environment interaction occurs whereby the benefits of familial excess longevity are more available to those who have occupations with more autonomy and greater economic resources and/or opportunities for physical activity.

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Balland, Fabrice, Alexandre Boumezoued, Laurent Devineau, Marine Habart, and Tom Popa. "Mortality data reliability in an internal model." Annals of Actuarial Science 14, no. 2 (August 3, 2020): 420–44. http://dx.doi.org/10.1017/s1748499520000081.

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AbstractIn this paper, we discuss the impact of some mortality data anomalies on an internal model capturing longevity risk in the Solvency 2 framework. In particular, we are concerned with abnormal cohort effects such as those for generations 1919 and 1920, for which the period tables provided by the Human Mortality Database show particularly low and high mortality rates, respectively. To provide corrected tables for the three countries of interest here (France, Italy and West Germany), we use the approach developed by Boumezoued for countries for which the method applies (France and Italy) and provide an extension of the method for West Germany as monthly fertility histories are not sufficient to cover the generations of interest. These mortality tables are crucial inputs to stochastic mortality models forecasting future scenarios, from which the extreme 0.5% longevity improvement can be extracted, allowing for the calculation of the solvency capital requirement. More precisely, to assess the impact of such anomalies in the Solvency II framework, we use a simplified internal model based on three usual stochastic models to project mortality rates in the future combined with a closure table methodology for older ages. Correcting this bias obviously improves the data quality of the mortality inputs, which is of paramount importance today, and slightly decreases the capital requirement. Overall, the longevity risk assessment remains stable, as well as the selection of the stochastic mortality model. As a collateral gain of this data quality improvement, the more regular estimated parameters allow for new insights and a refined assessment regarding longevity risk.

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Richards, S. J., and I. D. Currie. "Longevity Risk and Annuity Pricing with the Lee-Carter Model." British Actuarial Journal 15, no. 2 (July 2009): 317–43. http://dx.doi.org/10.1017/s1357321700005675.

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ABSTRACTSeveral important classes of liability are sensitive to the direction of future mortality trends, and this paper presents some recent developments in fitting smooth models to historical mortality-experience data. We demonstrate the impact these models have on mortality projections, and the resulting impact which these projections have on financial products. We base our work round the Lee-Carter family of models. We find that each model fit, while using the same data and staying within the Lee-Carter family, can change the direction of the mortality projections. The main focus of the paper is to demonstrate the impact of these projections on various financial calculations, and we provide a number of ways of quantifying, both graphically and numerically, the model risk in such calculations. We conclude that the impact of our modelling assumptions is financially material. In short, there is a need for awareness of model risk when assessing longevity-related liabilities, especially for annuities and pensions.

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DENUIT, M., S. HABERMAN, and A. E. RENSHAW. "Longevity-contingent deferred life annuities." Journal of Pension Economics and Finance 14, no. 3 (January 13, 2015): 315–27. http://dx.doi.org/10.1017/s147474721400050x.

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AbstractConsidering the substantial systematic longevity risk threatening annuity providers’ solvency, indexing benefits on actual mortality improvements appears to be an efficient risk management tool, as discussed in Denuit et al. (2011) and Richter and Weber (2011). Whereas these papers consider indexing annuity payments, the present work suggests that the length of the deferment period could also be subject to revision, providing longevity-contingent deferred life annuities.

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Li, Han, and Qihe Tang. "ANALYZING MORTALITY BOND INDEXES VIA HIERARCHICAL FORECAST RECONCILIATION." ASTIN Bulletin 49, no. 3 (July 3, 2019): 823–46. http://dx.doi.org/10.1017/asb.2019.19.

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AbstractIn recent decades, there has been significant growth in the capital market for mortality- and longevity-linked bonds. Therefore, modeling and forecasting the mortality indexes underlying these bonds have crucial implications for risk management in life insurance companies. In this paper, we propose a hierarchical reconciliation approach to constructing probabilistic forecasts for mortality bond indexes. We apply this approach to analyzing the Swiss Re Kortis bond, which is the first “longevity trend bond” introduced in the market. We express the longevity divergence index associated with the bond’s principal reduction factor (PRF) in a hierarchical setting. We first adopt time-series models to obtain forecasts on each hierarchical level, and then apply a minimum trace reconciliation approach to ensure coherence of forecasts across all levels. Based on the reconciled probabilistic forecasts of the longevity divergence index, we estimate the probability distribution of the PRF of the Kortis bond, and compare our results with those stated in Standard and Poor’s report on pre-sale information. We also illustrate the strong performance of the approach by comparing the reconciled forecasts with unreconciled forecasts as well as those from the bottom-up approach and the optimal combination approach. Finally, we provide first insights on the interest spread of the Kortis bond throughout its risk period 2010–2016.

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Richards, S. J., I. D. Currie, and G. P. Ritchie. "A Value-at-Risk framework for longevity trend risk." British Actuarial Journal 19, no. 1 (January 25, 2013): 116–39. http://dx.doi.org/10.1017/s1357321712000451.

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AbstractLongevity risk faced by annuity portfolios and defined-benefit pension schemes is typically long-term, i.e. the risk is of an adverse trend which unfolds over a long period of time. However, there are circumstances when it is useful to know by how much expectations of future mortality rates might change over a single year. Such an approach lies at the heart of the one-year, value-at-risk view of reserves, and also for the pending Solvency II regime for insurers in the European Union. This paper describes a framework for determining how much a longevity liability might change based on new information over the course of one year. It is a general framework and can accommodate a wide choice of stochastic projection models, thus allowing the user to explore the importance of model risk. A further benefit of the framework is that it also provides a robustness test for projection models, which is useful in selecting an internal model for management purposes.

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Browne, B., J. Duchassaing, and F. Suter. "Longevity: A ‘Simple’ Stochastic Modelling of Mortality." British Actuarial Journal 15, S1 (2009): 249–65. http://dx.doi.org/10.1017/s1357321700005596.

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ABSTRACTAll UK insurers exposed to longevity risk need to perform stress tests for their Individual Capital Assessment (ICA). Some have put in place deterministic models which are arguably too simple; others have developed stochastic models that can be demanding and complex.This paper presents a simple model to turn any deterministic mortality scenario into a stochastic model. We propose a simple model of stochastic variation that is easy to explain and to implement, which could be an alternative to and/or complete some of the well known models. The model can be applied to any best estimates of future mortality rates, as it aims to describe how longevity behaves around the projected expected values.The paper proposes a possible calibration on the England and Wales population mortality that produces a minimum indication of possible future variation and uses the results to validate the model's assumptions. Using sample portfolios and the stochastic model, we can simulate cash flows to determine the distribution of the net present values (NPV) of annuity outgo.

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Li, Hong. "DYNAMIC HEDGING OF LONGEVITY RISK: THE EFFECT OF TRADING FREQUENCY." ASTIN Bulletin 48, no. 1 (August 31, 2017): 197–232. http://dx.doi.org/10.1017/asb.2017.26.

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AbstractThis paper investigates dynamic hedging strategies for pension and annuity liabilities that are exposed to longevity risk. In particular, we consider a hedger who wishes to minimize the variance of her hedging error using index-based longevity-linked derivatives. To cope with the fact that liquidity of longevity-linked derivatives is still limited, we consider a liquidity constrained case where the hedger can only trade longevity-linked derivatives at a frequency lower than other assets. Time-consistent, closed-form solutions of optimal hedging strategies are obtained under a forward mortality framework. In the numerical illustration, we show that lowering the trading of the longevity-linked derivatives to a 2-year frequency only leads to a slight loss of the hedging performance. Moreover, even when the longevity-linked derivatives are traded at a very low (5-year) frequency, dynamic hedging strategies still significantly outperform the static one.

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Alvarez, Jesús-Adrián, Francisco Villavicencio, Cosmo Strozza, and Carlo Giovanni Camarda. "Regularities in human mortality after age 105." PLOS ONE 16, no. 7 (July 14, 2021): e0253940. http://dx.doi.org/10.1371/journal.pone.0253940.

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Empirical research on human mortality and extreme longevity suggests that the risk of death among the oldest-old ceases to increase and levels off at age 110. The universality of this finding remains in dispute because of two main reasons: i) high uncertainty around statistical estimates generated from scarce data, and ii) the lack of country-specific comparisons. In this article, we estimate age patterns of mortality above age 105 using data from the International Database on Longevity, an exceptionally large and recently updated database comprising more than 13,000 validated records of long-lived individuals from eight populations. We show that, in all of them, similar mortality trajectories arise, suggesting that the risk of dying levels off after age 105. As more high-quality data become available, there is more evidence in support of a levelling-off of the risk of dying as a regularity of longevous populations.

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Ben Salah, Sana, and Lotfi Belkacem. "On The Longevity Risk Assessment Under Solvency II." Journal of Applied Business Research (JABR) 31, no. 3 (May 4, 2015): 1149. http://dx.doi.org/10.19030/jabr.v31i3.9238.

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<p>This paper deals with the longevity risk assessment within the Solvency II framework. We propose a methodology allowing obtaining longevity shocks specified by gender, age and maturity. These shocks, which are calibrated on experience mortality data relative to a French insurance company, are proved to be far away from that assumed in the standard formula and the resulting solvency capital requirement (SCR) leads to significant capital savings as compared to the standard approach.</p>

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Ngugnie Diffouo, Pauline Milaure, and Pierre Devolder. "Longevity Risk Measurement of Life Annuity Products." Risks 8, no. 1 (March 18, 2020): 31. http://dx.doi.org/10.3390/risks8010031.

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This paper captures and measures the longevity risk generated by an annuity product. The longevity risk is materialized by the uncertain level of the future liability compared to the initially foretasted or expected value. Herein we compute the solvency capital (SC) of an insurer selling such a product within a single risk setting for three different life annuity products. Within the Solvency II framework, we capture the mortality of policyholders by the mean of the Hull–White model. Using the numerical analysis, we identify the product that requires the most SC from an insurer and the most profitable product for a shareholder. For policyholders we identify the cheapest product by computing the premiums and the most profitable product by computing the benefit levels. We further study how sensitive the SC is with respect to some significant parameters.

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Liu, Liqun. "Spillover of cause-specific longevity interventions: an independent mortality risk model." European Journal of Health Economics 9, no. 2 (June 5, 2007): 193–201. http://dx.doi.org/10.1007/s10198-007-0060-7.

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Yang, Sharon S., and Chou-Wen Wang. "Pricing and securitization of multi-country longevity risk with mortality dependence." Insurance: Mathematics and Economics 52, no. 2 (March 2013): 157–69. http://dx.doi.org/10.1016/j.insmatheco.2012.10.004.

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Lin, Tzuling, and Cary Chi-Liang Tsai. "Hedging Mortality/Longevity Risks for Multiple Years." North American Actuarial Journal 24, no. 1 (September 20, 2019): 118–40. http://dx.doi.org/10.1080/10920277.2019.1625789.

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Journal articles on the topic 'Longevity and mortality risk'

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