Pub Date : 2022-07-13DOI: 10.1017/S1748499522000094
Maria Carannante, V. D'Amato, S. Haberman
Abstract The Covid-19 pandemic caused an alarming mortality stress. The evidence shows that a significant proportion of people who die from Covid-19 are in a frail state. According to this consideration, we assume that the mortality shocks are related to a group of the individuals with some co-morbidities at Covid-19 diagnosis. In other words, the mortality shocks present a specific characterisation, which consists of a causal connection with pre-existing conditions, and the phenomenon could be described as a mortality acceleration. In this paper, an Accelerated Mortality Model is proposed in order to capture the different effects on mortality that depend on the evolution of the pandemic and the presence of co-morbidities at diagnosis. Furthermore, we assess the impact of Covid-19 mortality acceleration on a set of traditional life insurance contracts. We observe that, although mortality acceleration by Covid-19 affects more markedly the elderly and unhealthy sub-populations, it could be considered as a temporary shock with a limited impact on the life insurance market.
{"title":"COVID-19 accelerated mortality shocks and the impact on life insurance: the Italian situation","authors":"Maria Carannante, V. D'Amato, S. Haberman","doi":"10.1017/S1748499522000094","DOIUrl":"https://doi.org/10.1017/S1748499522000094","url":null,"abstract":"Abstract The Covid-19 pandemic caused an alarming mortality stress. The evidence shows that a significant proportion of people who die from Covid-19 are in a frail state. According to this consideration, we assume that the mortality shocks are related to a group of the individuals with some co-morbidities at Covid-19 diagnosis. In other words, the mortality shocks present a specific characterisation, which consists of a causal connection with pre-existing conditions, and the phenomenon could be described as a mortality acceleration. In this paper, an Accelerated Mortality Model is proposed in order to capture the different effects on mortality that depend on the evolution of the pandemic and the presence of co-morbidities at diagnosis. Furthermore, we assess the impact of Covid-19 mortality acceleration on a set of traditional life insurance contracts. We observe that, although mortality acceleration by Covid-19 affects more markedly the elderly and unhealthy sub-populations, it could be considered as a temporary shock with a limited impact on the life insurance market.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"478 - 497"},"PeriodicalIF":1.7,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43374136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-01DOI: 10.1017/S1748499522000070
P. Embrechts
From a regulatory point of view, pandemic risk was clearly on the table, be it either through stress tests for mortality rates, so-called pandemic shocks, or a requirement for concrete continuity plans in the case of serious business interruption. [...]various publications stress the fact that flu pandemics occur more frequently than we think (Marani et al., 2021). Through a shared IT infrastructure between suppliers, manufacturers, distributors, retailers, auditors, consumers and, of course, insurers3, blockchain technology enabled a considerable growth in supply chain management. Examples include supply chain insurance, crop insurance, longevity bonds, the evolving world of catastrophe insurance, pandemic bonds, parametric insurance, innovative pension schemes in a historically low interest rate environment, and the always-present market for insurance-linked securities.
{"title":"Editorial The walls came tumbling down","authors":"P. Embrechts","doi":"10.1017/S1748499522000070","DOIUrl":"https://doi.org/10.1017/S1748499522000070","url":null,"abstract":"From a regulatory point of view, pandemic risk was clearly on the table, be it either through stress tests for mortality rates, so-called pandemic shocks, or a requirement for concrete continuity plans in the case of serious business interruption. [...]various publications stress the fact that flu pandemics occur more frequently than we think (Marani et al., 2021). Through a shared IT infrastructure between suppliers, manufacturers, distributors, retailers, auditors, consumers and, of course, insurers3, blockchain technology enabled a considerable growth in supply chain management. Examples include supply chain insurance, crop insurance, longevity bonds, the evolving world of catastrophe insurance, pandemic bonds, parametric insurance, innovative pension schemes in a historically low interest rate environment, and the always-present market for insurance-linked securities.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"211 - 213"},"PeriodicalIF":1.7,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48401920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-09DOI: 10.1017/S1748499522000069
Jennifer Alonso-García
Exactly 11 years ago, Sweeting (2011) noted in his Editorial that “Even with the uncertainties around the choices of models and parameters, [stochastic mortality modeling] can be used to give a probabilistic assessment of the range of outcomes”. A quick read through past issues of Annals of Actuarial Science shows us that mortality modelling is still a hot topic in actuarial science, as evidenced in the multiple papers that have aimed at innovating towards the most suitable mathematical frameworks and model specifications. The past three decades have been characterised by a myriad of developments, Li & Lee (2005), Cairns et al. (2006), Renshaw & Haberman (2006) to cite a few, raising the need for a useful overview in both modelling and forecasting. Booth & Tickle (2008), in their exhaustive work, review the main methodological developments in (stochastic) mortality modelling from 1980 onwards focusing not only on Lee–Carter or GLM-based methodologies but also on parametric models and old-age mortality. In the same vein, Li (2014) focuses exclusively on simulation strategies. After sticking to a Lee & Carter (1992) model, and given the explosion of scientific papers focusing on how to best account for forecasting uncertainty, Li (2014) asks the simple question: What is the best performing simulation strategy? The answer is: it depends on the model fit; furthermore the choice of forecasting procedure matters. Clearly, attention has to be put into how the base model fits the data before focusing on the forecast. If there are unusual patterns in the residuals caused, e.g. by a non-captured cohort effect, the results produced by different simulation techniques could vary substantially. There is consensus about residuals needing to be pattern-free for a model to be well performing. This observation motivated Renshaw & Haberman (2006) to generalize the classical Lee & Carter (1992) model, adding a cohort component. They show that adding such a cohort effect renders the residual plots pattern-free. However, since cohort is directly related to age and period, identifiability issues arise due to the collinearity between these three parameters. This could be particularly problematic when projecting future mortality rates. Hunt & Blake (2020) focus on this particular issue. They highlight that some identifiability constraints are arbitrary and have an impact on the trend of particular parameters. Hence, they propose to determine which features of the parameters are data driven or choice driven. Based only on the data-driven trends, a selection for the time series should be done, ensuring that the forecast does not depend on arbitrary choices. Another way of studying mortality is not by extrapolating aggregate trends with a suitable model, but by studying the underlying causes of death. This allows for an analysis of causal mortality, as well as the dependence between different competing causes. Indeed, if you die from cardiovascular disease, you simply canno
{"title":"AAS Thematic issue: “Mortality: from Lee–Carter to AI”","authors":"Jennifer Alonso-García","doi":"10.1017/S1748499522000069","DOIUrl":"https://doi.org/10.1017/S1748499522000069","url":null,"abstract":"Exactly 11 years ago, Sweeting (2011) noted in his Editorial that “Even with the uncertainties around the choices of models and parameters, [stochastic mortality modeling] can be used to give a probabilistic assessment of the range of outcomes”. A quick read through past issues of Annals of Actuarial Science shows us that mortality modelling is still a hot topic in actuarial science, as evidenced in the multiple papers that have aimed at innovating towards the most suitable mathematical frameworks and model specifications. The past three decades have been characterised by a myriad of developments, Li & Lee (2005), Cairns et al. (2006), Renshaw & Haberman (2006) to cite a few, raising the need for a useful overview in both modelling and forecasting. Booth & Tickle (2008), in their exhaustive work, review the main methodological developments in (stochastic) mortality modelling from 1980 onwards focusing not only on Lee–Carter or GLM-based methodologies but also on parametric models and old-age mortality. In the same vein, Li (2014) focuses exclusively on simulation strategies. After sticking to a Lee & Carter (1992) model, and given the explosion of scientific papers focusing on how to best account for forecasting uncertainty, Li (2014) asks the simple question: What is the best performing simulation strategy? The answer is: it depends on the model fit; furthermore the choice of forecasting procedure matters. Clearly, attention has to be put into how the base model fits the data before focusing on the forecast. If there are unusual patterns in the residuals caused, e.g. by a non-captured cohort effect, the results produced by different simulation techniques could vary substantially. There is consensus about residuals needing to be pattern-free for a model to be well performing. This observation motivated Renshaw & Haberman (2006) to generalize the classical Lee & Carter (1992) model, adding a cohort component. They show that adding such a cohort effect renders the residual plots pattern-free. However, since cohort is directly related to age and period, identifiability issues arise due to the collinearity between these three parameters. This could be particularly problematic when projecting future mortality rates. Hunt & Blake (2020) focus on this particular issue. They highlight that some identifiability constraints are arbitrary and have an impact on the trend of particular parameters. Hence, they propose to determine which features of the parameters are data driven or choice driven. Based only on the data-driven trends, a selection for the time series should be done, ensuring that the forecast does not depend on arbitrary choices. Another way of studying mortality is not by extrapolating aggregate trends with a suitable model, but by studying the underlying causes of death. This allows for an analysis of causal mortality, as well as the dependence between different competing causes. Indeed, if you die from cardiovascular disease, you simply canno","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"17 1","pages":"212 - 214"},"PeriodicalIF":1.7,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42499802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-24DOI: 10.1017/S1748499522000033
Rui Zhou, J. S. Li
Abstract There has been a growing interest among pension plan sponsors in envisioning how the mortality experience of their active and deferred members may turn out to be if a pandemic similar to the COVID-19 occurs in the future. To address their needs, we propose in this paper a stochastic model for simulating future mortality scenarios with COVID-alike effects. The proposed model encompasses three parameter levels. The first level includes parameters that capture the long-term pattern of mortality, whereas the second level contains parameters that gauge the excess age-specific mortality due to COVID-19. Parameters in the first and second levels are estimated using penalised quasi-likelihood maximisation method which was proposed for generalised linear mixed models. Finally, the third level includes parameters that draw on expert opinions concerning, for example, how likely a COVID-alike pandemic will occur in the future. We illustrate our proposed model with data from the United States and a range of expert opinions.
{"title":"A multi-parameter-level model for simulating future mortality scenarios with COVID-alike effects","authors":"Rui Zhou, J. S. Li","doi":"10.1017/S1748499522000033","DOIUrl":"https://doi.org/10.1017/S1748499522000033","url":null,"abstract":"Abstract There has been a growing interest among pension plan sponsors in envisioning how the mortality experience of their active and deferred members may turn out to be if a pandemic similar to the COVID-19 occurs in the future. To address their needs, we propose in this paper a stochastic model for simulating future mortality scenarios with COVID-alike effects. The proposed model encompasses three parameter levels. The first level includes parameters that capture the long-term pattern of mortality, whereas the second level contains parameters that gauge the excess age-specific mortality due to COVID-19. Parameters in the first and second levels are estimated using penalised quasi-likelihood maximisation method which was proposed for generalised linear mixed models. Finally, the third level includes parameters that draw on expert opinions concerning, for example, how likely a COVID-alike pandemic will occur in the future. We illustrate our proposed model with data from the United States and a range of expert opinions.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"453 - 477"},"PeriodicalIF":1.7,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46293888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-10DOI: 10.1017/s1748499522000045
Simon Schnürch, Torsten Kleinow, Ralf Korn, Andreas Wagner
The COVID-19 pandemic interrupts the relatively steady trend of improving longevity observed in many countries over the last decades. We claim that this needs to be addressed explicitly in many mortality modelling applications, for example, in the life insurance industry. To support this position, we provide a descriptive analysis of the mortality development of several countries up to and including the year 2020. Furthermore, we perform an empirical and theoretical investigation of the impact a mortality jump has on the parameters, forecasts and implied present values of the popular Lee–Carter mortality model. We find that COVID-19 has resulted in substantial mortality shocks in many countries. We show that such shocks have a large impact on point and interval forecasts of death rates and, consequently, on the valuation of mortality-related insurance products. We obtain similar findings under the Cairns–Blake–Dowd mortality model, which demonstrates that the effects caused by COVID-19 show up in a variety of models. Finally, we provide an overview of approaches to handle extreme mortality events such as the COVID-19 pandemic in mortality modelling.
{"title":"The impact of mortality shocks on modelling and insurance valuation as exemplified by COVID-19","authors":"Simon Schnürch, Torsten Kleinow, Ralf Korn, Andreas Wagner","doi":"10.1017/s1748499522000045","DOIUrl":"https://doi.org/10.1017/s1748499522000045","url":null,"abstract":"<p>The COVID-19 pandemic interrupts the relatively steady trend of improving longevity observed in many countries over the last decades. We claim that this needs to be addressed explicitly in many mortality modelling applications, for example, in the life insurance industry. To support this position, we provide a descriptive analysis of the mortality development of several countries up to and including the year 2020. Furthermore, we perform an empirical and theoretical investigation of the impact a mortality jump has on the parameters, forecasts and implied present values of the popular Lee–Carter mortality model. We find that COVID-19 has resulted in substantial mortality shocks in many countries. We show that such shocks have a large impact on point and interval forecasts of death rates and, consequently, on the valuation of mortality-related insurance products. We obtain similar findings under the Cairns–Blake–Dowd mortality model, which demonstrates that the effects caused by COVID-19 show up in a variety of models. Finally, we provide an overview of approaches to handle extreme mortality events such as the COVID-19 pandemic in mortality modelling.</p>","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"126 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-08DOI: 10.1017/s1748499523000155
Benjamin Avanzi, Mark Lavender, G. Taylor, Bernard Wong
Traditional techniques for calculating outstanding claim liabilities such as the chain-ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck & Debruyne (2011, Insurance: Mathematics and Economics, 48, 85–98) and Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). In this paper, we put forward two alternative robust bivariate chain-ladder techniques to extend the approach of Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). The first technique is based on Adjusted Outlyingness (Hubert & Van der Veeken, 2008. Journal of Chemometrics,22, 235–246) and explicitly incorporates skewness into the analysis while providing a unique measure of outlyingness for each observation. The second technique is based on bagdistance (Hubert et al., 2016. Statistics: Methodology, 1–23) which is derived from the bagplot; however; it is able to provide a unique measure of outlyingness and a means to adjust outlying observations based on this measure. Furthermore, we extend our robust bivariate chain-ladder approach to an N-dimensional framework. The implementation of the methods, especially beyond bivariate, is not trivial. This is illustrated on a trivariate data set from Australian general insurers and results under the different outlier detection and treatment mechanisms are compared.
众所周知，计算未偿索赔负债的传统方法，如链梯法，存在被过去索赔数据中的异常值扭曲的风险。不幸的是，除了Verdonck & Debruyne (2011, Insurance: Mathematics and Economics, 48, 85-98)和Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188-193)等显著的例外，关于稳健储备方法的文献很少。在本文中，我们提出了两种可选的鲁棒二元链梯技术来扩展Verdonck和Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188-193)的方法。第一种技术是基于调整的离群度(Hubert & Van der Veeken, 2008)。化学计量学杂志，22,235-246)，并明确地将偏度纳入分析，同时为每个观察提供独特的离群度测量。第二种技术是基于包距(Hubert et al.， 2016)。统计:方法，1-23)，来源于袋图;然而;它能够提供一种独特的离群度度量和一种基于该度量调整离群观测值的方法。此外，我们将我们的鲁棒二元链梯方法扩展到n维框架。这些方法的实现，特别是超越二元变量的实现，不是微不足道的。这是由澳大利亚一般保险公司的三变量数据集说明的，并比较了不同异常值检测和治疗机制下的结果。
{"title":"Detection and treatment of outliers for multivariate robust loss reserving","authors":"Benjamin Avanzi, Mark Lavender, G. Taylor, Bernard Wong","doi":"10.1017/s1748499523000155","DOIUrl":"https://doi.org/10.1017/s1748499523000155","url":null,"abstract":"\u0000 Traditional techniques for calculating outstanding claim liabilities such as the chain-ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck & Debruyne (2011, Insurance: Mathematics and Economics, 48, 85–98) and Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). In this paper, we put forward two alternative robust bivariate chain-ladder techniques to extend the approach of Verdonck & Van Wouwe (2011, Insurance: Mathematics and Economics,49, 188–193). The first technique is based on Adjusted Outlyingness (Hubert & Van der Veeken, 2008. Journal of Chemometrics,22, 235–246) and explicitly incorporates skewness into the analysis while providing a unique measure of outlyingness for each observation. The second technique is based on bagdistance (Hubert et al., 2016. Statistics: Methodology, 1–23) which is derived from the bagplot; however; it is able to provide a unique measure of outlyingness and a means to adjust outlying observations based on this measure.\u0000 Furthermore, we extend our robust bivariate chain-ladder approach to an N-dimensional framework. The implementation of the methods, especially beyond bivariate, is not trivial. This is illustrated on a trivariate data set from Australian general insurers and results under the different outlier detection and treatment mechanisms are compared.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49020139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-21DOI: 10.1017/s1748499521000257
Ou Dang, Mingbin Feng, Mary R. Hardy
Estimating tail risk measures for portfolios of complex variable annuities is an important enterprise risk management task which usually requires nested simulation. In the nested simulation, the outer simulation stage involves projecting scenarios of key risk factors under the real-world measure, while the inner simulations are used to value pay-offs under guarantees of varying complexity, under a risk-neutral measure. In this paper, we propose and analyse an efficient simulation approach that dynamically allocates the inner simulations to the specific outer scenarios that are most likely to generate larger losses. These scenarios are identified using a proxy calculation that is used only to rank the outer scenarios, not to estimate the tail risk measure directly. As the proxy ranking will not generally provide a perfect match to the true ranking of outer scenarios, we calculate a measure based on the concomitant of order statistics to test whether further tail scenarios are required to ensure, with given confidence, that the true tail scenarios are captured. This procedure, which we call the dynamic importance allocated nested simulation approach, automatically adjusts for the relationship between the proxy calculations and the true valuations and also signals when the proxy is not sufficiently accurate.
{"title":"Dynamic importance allocated nested simulation for variable annuity risk measurement","authors":"Ou Dang, Mingbin Feng, Mary R. Hardy","doi":"10.1017/s1748499521000257","DOIUrl":"https://doi.org/10.1017/s1748499521000257","url":null,"abstract":"<p>Estimating tail risk measures for portfolios of complex variable annuities is an important enterprise risk management task which usually requires nested simulation. In the nested simulation, the outer simulation stage involves projecting scenarios of key risk factors under the real-world measure, while the inner simulations are used to value pay-offs under guarantees of varying complexity, under a risk-neutral measure. In this paper, we propose and analyse an efficient simulation approach that dynamically allocates the inner simulations to the specific outer scenarios that are most likely to generate larger losses. These scenarios are identified using a proxy calculation that is used only to rank the outer scenarios, not to estimate the tail risk measure directly. As the proxy ranking will not generally provide a perfect match to the true ranking of outer scenarios, we calculate a measure based on the concomitant of order statistics to test whether further tail scenarios are required to ensure, with given confidence, that the true tail scenarios are captured. This procedure, which we call the dynamic importance allocated nested simulation approach, automatically adjusts for the relationship between the proxy calculations and the true valuations and also signals when the proxy is not sufficiently accurate.</p>","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"32 8","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-21DOI: 10.1017/S1748499522000021
S. Richards
Abstract The COVID-19 pandemic requires that actuaries track short-term mortality fluctuations in the portfolios they manage. This demands methods that not only operate over much shorter time periods than a year but that also deal with reporting delays. In this paper, we consider a semi-parametric approach for tracking portfolio mortality levels in continuous time. We identify both seasonal patterns and mortality shocks, thus providing a comparison benchmark for the impact of COVID-19 in terms of a portfolio’s own past experience. A parametric model is presented to allow for the average impact of seasonal variation and also reporting delays. We find that an estimate of mortality reporting delays can be made from a single extract of experience data. This can be used to forecast unreported deaths and improve estimates of recent mortality levels. Results are given for annuity portfolios in France, the UK and the USA.
{"title":"Real-time measurement of portfolio mortality levels in the presence of shocks and reporting delays","authors":"S. Richards","doi":"10.1017/S1748499522000021","DOIUrl":"https://doi.org/10.1017/S1748499522000021","url":null,"abstract":"Abstract The COVID-19 pandemic requires that actuaries track short-term mortality fluctuations in the portfolios they manage. This demands methods that not only operate over much shorter time periods than a year but that also deal with reporting delays. In this paper, we consider a semi-parametric approach for tracking portfolio mortality levels in continuous time. We identify both seasonal patterns and mortality shocks, thus providing a comparison benchmark for the impact of COVID-19 in terms of a portfolio’s own past experience. A parametric model is presented to allow for the average impact of seasonal variation and also reporting delays. We find that an estimate of mortality reporting delays can be made from a single extract of experience data. This can be used to forecast unreported deaths and improve estimates of recent mortality levels. Results are given for annuity portfolios in France, the UK and the USA.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"430 - 452"},"PeriodicalIF":1.7,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48970111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-18DOI: 10.1017/S1748499521000270
Saman Vahabi, Amir T. Payandeh Najafabadi
Abstract This paper obtains an optimal strategy in a finite horizon time for a portfolio of a defined contribution (DC) pension fund for an investor with the CRRA utility function. It employs the optimal stochastic control method in a financial market with two different asset markets, one risk-free and another one risky asset in which its jump follows either by a finite or infinite activity Lévy process. Sensitivity of jump parameters in an uncertainty financial market has been studied.
{"title":"Optimal investment strategy for a DC pension fund plan in a finite horizon time: an optimal stochastic control approach","authors":"Saman Vahabi, Amir T. Payandeh Najafabadi","doi":"10.1017/S1748499521000270","DOIUrl":"https://doi.org/10.1017/S1748499521000270","url":null,"abstract":"Abstract This paper obtains an optimal strategy in a finite horizon time for a portfolio of a defined contribution (DC) pension fund for an investor with the CRRA utility function. It employs the optimal stochastic control method in a financial market with two different asset markets, one risk-free and another one risky asset in which its jump follows either by a finite or infinite activity Lévy process. Sensitivity of jump parameters in an uncertainty financial market has been studied.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"367 - 383"},"PeriodicalIF":1.7,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45221015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-09DOI: 10.1017/S1748499521000282
V. Djeundje
Abstract Modelling and forecasting mortality is a topic of crucial importance to actuaries and demographers. However, forecasts from the majority of mortality projection models are continuations of past trends seen in the data. As such, these models are unable to account for external opinions or expert judgement. In this work, we present a method for the incorporation of deterministic opinions into the smoothing and forecasting of mortality rates using constraints. Not only does our approach yield a smooth transition from the past into the future, but also, the shapes of the resulting forecasts are governed by a combination of the opinion inputs and the speed of improvements observed in the data. In addition, our approach offers the possibility to compute the amount of uncertainty around the projected mortality trends conditional on the opinion inputs, and this allows us to highlight some of the pitfalls of deterministic projection methods.
{"title":"On the integration of deterministic opinions into mortality smoothing and forecasting","authors":"V. Djeundje","doi":"10.1017/S1748499521000282","DOIUrl":"https://doi.org/10.1017/S1748499521000282","url":null,"abstract":"Abstract Modelling and forecasting mortality is a topic of crucial importance to actuaries and demographers. However, forecasts from the majority of mortality projection models are continuations of past trends seen in the data. As such, these models are unable to account for external opinions or expert judgement. In this work, we present a method for the incorporation of deterministic opinions into the smoothing and forecasting of mortality rates using constraints. Not only does our approach yield a smooth transition from the past into the future, but also, the shapes of the resulting forecasts are governed by a combination of the opinion inputs and the speed of improvements observed in the data. In addition, our approach offers the possibility to compute the amount of uncertainty around the projected mortality trends conditional on the opinion inputs, and this allows us to highlight some of the pitfalls of deterministic projection methods.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"384 - 400"},"PeriodicalIF":1.7,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47397258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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