Pub Date : 2022-11-01DOI: 10.1017/s1748499522000185
M. Edwards
The analysis of risk (in particular, mortality, morbidity, or equivalent non-life claims incidence), and associated risk management;The mathematics of finance;Developing models of future relating to contingent events (typically, cash flow models), and related aspects such as an appreciation of model risk, and a mature approach to model validation. [...]in my field of work in the context of demographic risk, assumption setting, and the development of capital models in the UK and across EMEA, I have been surprised by the lack of interest and activity to date in considering how the pandemic might reasonably change our views of the future – whether best estimate or extreme scenarios. Overall, there are many ways that actuaries involved in life insurance and pension fund work in particular can help within their “formal” areas of expertise.
{"title":"How actuarial perspectives can help in a pandemic","authors":"M. Edwards","doi":"10.1017/s1748499522000185","DOIUrl":"https://doi.org/10.1017/s1748499522000185","url":null,"abstract":"The analysis of risk (in particular, mortality, morbidity, or equivalent non-life claims incidence), and associated risk management;The mathematics of finance;Developing models of future relating to contingent events (typically, cash flow models), and related aspects such as an appreciation of model risk, and a mature approach to model validation. [...]in my field of work in the context of demographic risk, assumption setting, and the development of capital models in the UK and across EMEA, I have been surprised by the lack of interest and activity to date in considering how the pandemic might reasonably change our views of the future – whether best estimate or extreme scenarios. Overall, there are many ways that actuaries involved in life insurance and pension fund work in particular can help within their “formal” areas of expertise.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"428 - 429"},"PeriodicalIF":1.7,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49514472","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 : 2022-10-17DOI: 10.1017/s1748499522000173
Sixian Tang, Jackie Li, L. Tickle
One complication in mortality modelling is capturing the impact of risk factors that contribute to mortality differentials between different populations. Evidence has suggested that mortality differentials tend to diminish over age. Classical methods such as the Gompertz law attempt to capture mortality patterns over age using intercept and slope parameters, possibly causing an unjustified mortality crossover at advanced ages when applied independently to different populations. In recent research, Richards (Scandinavian Actuarial Journal2020(2), 110–127) proposed a Hermite spline (HS) model that describes the age pattern of mortality differentials using one parameter and circumvents an unreasonable crossover by default. The original HS model was applied to pension data at individual level in the age dimension only. This paper extends the method to model population mortality in both age and period dimensions. Our results indicate that in addition to possessing desirable fitting properties, the HS approach can produce accurate mortality forecasts, compared with the Gompertz and P-splines models.
{"title":"A Hermite spline approach for modelling population mortality","authors":"Sixian Tang, Jackie Li, L. Tickle","doi":"10.1017/s1748499522000173","DOIUrl":"https://doi.org/10.1017/s1748499522000173","url":null,"abstract":"\u0000 One complication in mortality modelling is capturing the impact of risk factors that contribute to mortality differentials between different populations. Evidence has suggested that mortality differentials tend to diminish over age. Classical methods such as the Gompertz law attempt to capture mortality patterns over age using intercept and slope parameters, possibly causing an unjustified mortality crossover at advanced ages when applied independently to different populations. In recent research, Richards (Scandinavian Actuarial Journal2020(2), 110–127) proposed a Hermite spline (HS) model that describes the age pattern of mortality differentials using one parameter and circumvents an unreasonable crossover by default. The original HS model was applied to pension data at individual level in the age dimension only. This paper extends the method to model population mortality in both age and period dimensions. Our results indicate that in addition to possessing desirable fitting properties, the HS approach can produce accurate mortality forecasts, compared with the Gompertz and P-splines models.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49505952","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 : 2022-10-07DOI: 10.1017/s1748499522000161
D. J. Crispin, S. M. Kinsley
Determining accurate capital requirements is a central activity across the life insurance industry. This is computationally challenging and often involves the acceptance of proxy errors that directly impact capital requirements. Within simulation-based capital models, where proxies are being used, capital estimates are approximations that contain both statistical and proxy errors. Here, we show how basic error analysis combined with targeted exact computation can entirely eliminate proxy errors from the capital estimate. Consideration of the possible ordering of losses, combined with knowledge of their error bounds, identifies an important subset of scenarios. When these scenarios are calculated exactly, the resulting capital estimate can be made devoid of proxy errors. Advances in the handling of proxy errors improve the accuracy of capital requirements.
{"title":"Eliminating proxy errors from capital estimates by targeted exact computation","authors":"D. J. Crispin, S. M. Kinsley","doi":"10.1017/s1748499522000161","DOIUrl":"https://doi.org/10.1017/s1748499522000161","url":null,"abstract":"\u0000 Determining accurate capital requirements is a central activity across the life insurance industry. This is computationally challenging and often involves the acceptance of proxy errors that directly impact capital requirements. Within simulation-based capital models, where proxies are being used, capital estimates are approximations that contain both statistical and proxy errors. Here, we show how basic error analysis combined with targeted exact computation can entirely eliminate proxy errors from the capital estimate. Consideration of the possible ordering of losses, combined with knowledge of their error bounds, identifies an important subset of scenarios. When these scenarios are calculated exactly, the resulting capital estimate can be made devoid of proxy errors. Advances in the handling of proxy errors improve the accuracy of capital requirements.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41778525","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 : 2022-09-30DOI: 10.1017/S174849952200015X
G. P. Clemente, Francesco Della Corte, N. Savelli
Abstract This paper provides a stochastic model, consistent with Solvency II and the Delegated Regulation, to quantify the capital requirement for demographic risk. In particular, we present a framework that models idiosyncratic and trend risks exploiting a risk theory approach in which results are obtained analytically. We apply the model to non-participating policies and quantify the Solvency Capital Requirement for the aforementioned risks in different time horizons.
{"title":"A stochastic model for capital requirement assessment for mortality and longevity risk, focusing on idiosyncratic and trend components","authors":"G. P. Clemente, Francesco Della Corte, N. Savelli","doi":"10.1017/S174849952200015X","DOIUrl":"https://doi.org/10.1017/S174849952200015X","url":null,"abstract":"Abstract This paper provides a stochastic model, consistent with Solvency II and the Delegated Regulation, to quantify the capital requirement for demographic risk. In particular, we present a framework that models idiosyncratic and trend risks exploiting a risk theory approach in which results are obtained analytically. We apply the model to non-participating policies and quantify the Solvency Capital Requirement for the aforementioned risks in different time horizons.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"16 1","pages":"527 - 546"},"PeriodicalIF":1.7,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47274426","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 : 2022-09-26DOI: 10.1017/s1748499522000148
Michael Fackler
The loss count distributions whose probabilities ultimately satisfy Panjer’s recursion were classified between 1981 and 2002; they split into six types, which look quite diverse. Yet, the distributions are closely related – we show that their probabilities emerge out of one formula: the binomial series. We propose a parameter change that leads to a unified, practical and intuitive, representation of the Panjer distributions and their parameter space. We determine the subsets of the parameter space where the probabilities are continuous functions of the parameters. Finally, we give an inventory of parameterisations used for Panjer distributions.
{"title":"Panjer class revisited: one formula for the distributions of the Panjer (a,b,n) class","authors":"Michael Fackler","doi":"10.1017/s1748499522000148","DOIUrl":"https://doi.org/10.1017/s1748499522000148","url":null,"abstract":"<p>The loss count distributions whose probabilities ultimately satisfy Panjer’s recursion were classified between 1981 and 2002; they split into six types, which look quite diverse. Yet, the distributions are closely related – we show that their probabilities emerge out of one formula: the binomial series. We propose a parameter change that leads to a unified, practical and intuitive, representation of the Panjer distributions and their parameter space. We determine the subsets of the parameter space where the probabilities are continuous functions of the parameters. Finally, we give an inventory of parameterisations used for Panjer distributions.</p>","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"120 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509567","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 : 2022-08-25DOI: 10.1017/S1748499522000124
D. Dickson
Abstract We derive formulae for the moments of the time of ruin in both ordinary and modified Sparre Andersen risk models without specifying either the inter-claim time distribution or the individual claim amount distribution. We illustrate the application of our results in the special case of exponentially distributed claims, as well as for the following ordinary models: the classical risk model, phase-type(2) risk models, and the Erlang( $mathscr{n}$ ) risk model. We also show how the key quantities for modified models can be found.
{"title":"The moments of the time of ruin in Sparre Andersen risk models","authors":"D. Dickson","doi":"10.1017/S1748499522000124","DOIUrl":"https://doi.org/10.1017/S1748499522000124","url":null,"abstract":"Abstract We derive formulae for the moments of the time of ruin in both ordinary and modified Sparre Andersen risk models without specifying either the inter-claim time distribution or the individual claim amount distribution. We illustrate the application of our results in the special case of exponentially distributed claims, as well as for the following ordinary models: the classical risk model, phase-type(2) risk models, and the Erlang( \u0000$mathscr{n}$\u0000 ) risk model. We also show how the key quantities for modified models can be found.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"17 1","pages":"63 - 82"},"PeriodicalIF":1.7,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46779557","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 : 2022-08-15DOI: 10.1017/s1748499522000136
Martin Bladt, Michel Fuino, A. Shemendyuk, J. Wagner
Abstract The financing of long-term care and the planning of care capacity are of increasing interest due to demographic changes and the ageing population in many countries. Since many care-intensive conditions begin to manifest at higher ages, a better understanding and assessment of the expected costs, required infrastructure, and number of qualified personnel are essential. To evaluate the overall burden of institutional care, we derive a model based on the duration of stay in dependence and the intensity of help provided to elderly individuals. This article aims to model both aspects using novel longitudinal data from nursing homes in the canton of Geneva in Switzerland. Our data contain comprehensive health and care information, including medical diagnoses, levels of dependence, and physical and psychological impairments on 21,758 individuals. We build an accelerated failure time model to study the influence of selected factors on the duration of care and a beta regression model to describe the intensity of care. We show that apart from age and gender, the duration of stay before death is mainly affected by the underlying diseases and the number of different diagnoses. Simultaneously, care intensity is driven by the individual level of dependence and specific limitations. Using both evaluations, we approximate the overall care severity for individual profiles. Our study sheds light on the relevant medical, physical, and psychological health indicators that need to be accounted for, not only by care providers but also by policy-makers and insurers.
{"title":"Modelling the burden of long-term care for institutionalised elderly based on care duration and intensity","authors":"Martin Bladt, Michel Fuino, A. Shemendyuk, J. Wagner","doi":"10.1017/s1748499522000136","DOIUrl":"https://doi.org/10.1017/s1748499522000136","url":null,"abstract":"Abstract The financing of long-term care and the planning of care capacity are of increasing interest due to demographic changes and the ageing population in many countries. Since many care-intensive conditions begin to manifest at higher ages, a better understanding and assessment of the expected costs, required infrastructure, and number of qualified personnel are essential. To evaluate the overall burden of institutional care, we derive a model based on the duration of stay in dependence and the intensity of help provided to elderly individuals. This article aims to model both aspects using novel longitudinal data from nursing homes in the canton of Geneva in Switzerland. Our data contain comprehensive health and care information, including medical diagnoses, levels of dependence, and physical and psychological impairments on 21,758 individuals. We build an accelerated failure time model to study the influence of selected factors on the duration of care and a beta regression model to describe the intensity of care. We show that apart from age and gender, the duration of stay before death is mainly affected by the underlying diseases and the number of different diagnoses. Simultaneously, care intensity is driven by the individual level of dependence and specific limitations. Using both evaluations, we approximate the overall care severity for individual profiles. Our study sheds light on the relevant medical, physical, and psychological health indicators that need to be accounted for, not only by care providers but also by policy-makers and insurers.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"17 1","pages":"83 - 117"},"PeriodicalIF":1.7,"publicationDate":"2022-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44030546","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 : 2022-08-01DOI: 10.1017/s1748499522000082
Filippo Siegenthaler
Abstract We propose a new estimator for the ultimate prediction uncertainty within the famous Mack’s distribution-free chain-ladder model, which can be proved to be unbiased (conditionally given the first triangle column) under some additional technical assumptions. A peculiar behaviour of the unbiased estimator is given by its possible negativity. This is a drawback which might be worth trading off for the unbiasedness property, since there is empirical evidence that the likelihood of a negative realisation is extremely low. This offers an alternative to the well-known Mack and BBMW formulas since the latters can be proved to be biased. However, we also show that this novel estimator, as well as the Mack and BBMW formulas, can (with non-negligible probability) materially fail to estimate the true uncertainty.
{"title":"Unbiased estimator for the ultimate claim prediction error in the chain-ladder model of Mack","authors":"Filippo Siegenthaler","doi":"10.1017/s1748499522000082","DOIUrl":"https://doi.org/10.1017/s1748499522000082","url":null,"abstract":"Abstract We propose a new estimator for the ultimate prediction uncertainty within the famous Mack’s distribution-free chain-ladder model, which can be proved to be unbiased (conditionally given the first triangle column) under some additional technical assumptions. A peculiar behaviour of the unbiased estimator is given by its possible negativity. This is a drawback which might be worth trading off for the unbiasedness property, since there is empirical evidence that the likelihood of a negative realisation is extremely low. This offers an alternative to the well-known Mack and BBMW formulas since the latters can be proved to be biased. However, we also show that this novel estimator, as well as the Mack and BBMW formulas, can (with non-negligible probability) materially fail to estimate the true uncertainty.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"17 1","pages":"118 - 144"},"PeriodicalIF":1.7,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44297304","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 : 2022-07-29DOI: 10.1017/S1748499522000100
J. Boucher
Abstract In recent papers, Bonus-Malus Scales (BMS) estimated using data have been considered as an alternative to longitudinal data and hierarchical data approaches to model the dependence between different contracts for the same insured. Those papers, however, did not discuss in detail how to construct and understand BMS models, and many of the BMS’s basic properties were not discussed. The first objective of this paper is to correct this situation by explaining the logic behind BMS models and by describing those properties. More particularly, we will explain how BMS models are linked with simple count regression models that have covariates associated with the past claims experience. This study could help actuaries to understand how and why they should use BMS models for experience rating. The second objective of this paper is to create artificial past claims history for each insured. This is done by combining recent panel data theory with BMS models. We show that this addition significantly improves the prediction capacity of the BMS and provides a temporary solution for insurers who do not have enough historical data. We apply the BMS model to real data from a major Canadian insurance company. Results are analysed deeply to identify specific aspects of the BMS model.
{"title":"Bonus-Malus Scale models: creating artificial past claims history","authors":"J. Boucher","doi":"10.1017/S1748499522000100","DOIUrl":"https://doi.org/10.1017/S1748499522000100","url":null,"abstract":"Abstract In recent papers, Bonus-Malus Scales (BMS) estimated using data have been considered as an alternative to longitudinal data and hierarchical data approaches to model the dependence between different contracts for the same insured. Those papers, however, did not discuss in detail how to construct and understand BMS models, and many of the BMS’s basic properties were not discussed. The first objective of this paper is to correct this situation by explaining the logic behind BMS models and by describing those properties. More particularly, we will explain how BMS models are linked with simple count regression models that have covariates associated with the past claims experience. This study could help actuaries to understand how and why they should use BMS models for experience rating. The second objective of this paper is to create artificial past claims history for each insured. This is done by combining recent panel data theory with BMS models. We show that this addition significantly improves the prediction capacity of the BMS and provides a temporary solution for insurers who do not have enough historical data. We apply the BMS model to real data from a major Canadian insurance company. Results are analysed deeply to identify specific aspects of the BMS model.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"17 1","pages":"36 - 62"},"PeriodicalIF":1.7,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41845809","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 : 2022-07-28DOI: 10.1017/S1748499522000112
K. Fergusson, E. Platen
Abstract This paper proposes a shift in the valuation and production of long-term annuities, away from the classical risk-neutral methodology towards a methodology using the real-world probability measure. The proposed production method is applied to three examples of annuity products, one having annual payments linked to a mortality index and the savings account and the others having annual payments linked to a mortality index and an equity index with a guarantee that is linked to the same mortality index and the savings account. Out-of-sample hedge simulations demonstrate the effectiveness of the proposed less-expensive production method. In contrast to classical risk-neutral production, which revolves around the savings account as reference unit, the long-term best-performing portfolio, the numéraire portfolio of the equity market, is employed as the fundamental reference unit in the production of the annuity. The numéraire portfolio is the strictly positive, tradable portfolio that when used as denominator or benchmark makes all benchmarked non-negative portfolios supermartingales. Under real-world valuation, the initial benchmarked value of a benchmarked contingent claim equals its real-world conditional expectation. The proposed real-world valuation and production can lead to significantly lower values of long-term annuities and their less-expensive production than suggested by the risk-neutral approach.
{"title":"Less-expensive long-term annuities linked to mortality, cash and equity","authors":"K. Fergusson, E. Platen","doi":"10.1017/S1748499522000112","DOIUrl":"https://doi.org/10.1017/S1748499522000112","url":null,"abstract":"Abstract This paper proposes a shift in the valuation and production of long-term annuities, away from the classical risk-neutral methodology towards a methodology using the real-world probability measure. The proposed production method is applied to three examples of annuity products, one having annual payments linked to a mortality index and the savings account and the others having annual payments linked to a mortality index and an equity index with a guarantee that is linked to the same mortality index and the savings account. Out-of-sample hedge simulations demonstrate the effectiveness of the proposed less-expensive production method. In contrast to classical risk-neutral production, which revolves around the savings account as reference unit, the long-term best-performing portfolio, the numéraire portfolio of the equity market, is employed as the fundamental reference unit in the production of the annuity. The numéraire portfolio is the strictly positive, tradable portfolio that when used as denominator or benchmark makes all benchmarked non-negative portfolios supermartingales. Under real-world valuation, the initial benchmarked value of a benchmarked contingent claim equals its real-world conditional expectation. The proposed real-world valuation and production can lead to significantly lower values of long-term annuities and their less-expensive production than suggested by the risk-neutral approach.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":"17 1","pages":"170 - 207"},"PeriodicalIF":1.7,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45007835","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：