Cette thèse est mue par la volonté de son auteur (et de son promoteur) de mettre en évidence combien le concept d'ingéniérie actuarielle est non seulement un concept actuel mais également porteur d'avenir pour l'actuariat. Dans ingéniérie, on entend ingénieur, soit un individu formé à l'application des sciences, dans le but de résoudre des problèmes technologiques concrets et complexes. Ces compétences, traditionnellement plutôt utilisées par l'industrie, sont ici mises au service de l'Actuariat. Nous espérons montrer combien un actuaire ouvert aux techniques récentes de la Statistique peut enrichir sa panoplie d'outils pour répondre aux questions toujours plus variées que pose la pratique. Car là est aussi un des messages de ce travail: montrer que ces développements récents sont loin d'être de pures gymnastiques intellectuelles mais offrent de réelles solutions ou alternatives valables à des problèmes connus. Avec pour bagage les modèles de régression non linéaires, nous nous promenons dans les différents domaines de l'Actuariat, abordant tout d'abord un aspect méthodologique. Ensuite, nous traitons de deux problèmes liés à la branche Non Vie : tarification géographique et échelles bonus-malus. Enfin, nous voyons comment des perspectives nouvelles peuvent également s'inscrire dans la branche Vie, à travers la problématique de la modélisation de la mortalité future. Il ne s'agit en aucun cas d'un inventaire exhaustif des possibilités récentes offertes par la Statistique à l'Actuariat, mais bien d'un tour d'horizon qui entend ouvrir des portes dans des domaines variés. Cette thèse est composée d'articles (rédigés en anglais) publiés dans des revues nationales et internationales.

隨著台灣經濟的大幅提升與保險的觀念在國內越來越盛行，許多的人都會選擇去投保，本研究採用的資料是從保險事業發展中心所獲得，其收集台灣各個保險公司所銷售的保單，包含定期險、生死合險和終身壽險的資料。我們藉由此資料來分析具有何種特質的人會去購買何種保單，哪些因素會造成死亡率之間的差異。近些年來，台灣的生活水準和醫療水平有顯著的進步，台灣人口的死亡率也因此大幅地下降，男女間的平均餘命也隨之增加，台灣逐步地邁向高齡化社會。但隨著死亡率的改善，保險公司之前所銷售的較長年期的保險商品，有可能會造成保險公司低估或高估其保費，使公司未來的現金流量不穩定。而且以前公司通常是使用生命表的死亡率為基礎，但這樣並不能真正反映有保險人口的死亡機率，因此，我們將使用實際投保的資料，透過Whittaker修勻和Gompertz法則，計算其死亡率，並利用Lee -Carter模型去對未來的死亡率做預測，探討死亡率的下降，會對保險公司造成何種衝擊與其影響到底會有多大。

This thesis analyses the COVID-19 pandemic’s effects on Swedish mortality during 2020 by investigating whether it has resulted in excess mortality. This is done using a stochastic mortality projection model from the Lee-Carter framework and by assuming the number of deaths follows a Poisson distribution. Due to the few confirmed COVID-19 deaths at younger ages, the decision is made to only include 50-to-100-year-olds in the analysis. Models in the Lee-Carter framework are fitted on historical data from 1993–2019 collected from Human Mortality Database and Statistiska Centralbyrån. After evaluating the models, inter alia using residual analysis and backtesting, we ascertain that the classical Lee-Carter model accomplishes a wanted level of fit and forecast accuracy. During the morality projection with the Lee-Carter model, three different sources of uncertainty are accounted for by constructing prediction intervals using bootstrap. The results show that the large age group 67–94-year-olds have suffered from statistically significant excess mortality during 2020. The level of excess mortality differs between ages, with the ages 70–90-year-olds having the highest number of excess deaths. Comparing the number of confirmed COVID-19 deaths to our forecasted number of excess deaths indicates the COVID-19 virus likely caused the surge in deaths.

<p>Under det gångna århundradet ökade den förväntade livslängden avsevärt såväl i Sverige som i övriga världen. 1900-talets förbättrade livslängd drevs inledningsvis av en minskad barnadödlighet medan de senare årtiondena kännetecknades av minskad dödlighet i höga åldrar.</p><p>En åldrande befolkning innebär ökade krav på sjukvård, äldreomsorg och inte minst pensionssystem. Pålitliga prognoser för vår framtida livslängd behövs för att beräkna de resurser som nämnda verksamheter kommer att ta i anspråk och utgör förutsättningen för en rättvis prissättning av försäkringsprodukter med levnadsrisk.</p><p>Lee-Carter-modellen är en av vår tids tongivande modeller för mortalitetsprognostisering. Modellen används här för att göra livslängdsprognoser utifrån svenska mortalitetsdata; prognoserna jämförs sedan med observerade utfall.</p><p>Mot bakgrund av resultatet diskuteras levnadsrisk med fokus på pensioner.</p><p>Inte oväntat presterar prognoserna ingen felfri bild av verkligheten och prognosfelet varierar i storlek mellan skattningarna; att använda dem som underlag för pensionsberäkningar hade i förlängningen varit ohållbart. Exemplet illustrerar på samma gång vår osäkerhet inför framtidens livslängdsutveckling och svårigheten i att prognostisera den.</p> / <p>During the past century, Sweden along with many other countries experienced a sharp decline in mortality rates. The increased life expectancy was initially propelled by mortality reductions among infants and subsequently by a survival improvement in advanced ages.</p><p>An ageing population has large implications for those providing services to the elderly, such as medical care and pensions, whilst also addressing the need for accurate and reliable mortality forecasts and projection methods.</p><p>The Lee-Carter model is the current gold standard for mortality forecasting and has been widely adopted in several studies. Here, the model is applied on Swedish mortality data; the projections are then compared to the observed lifespan development. Against this backdrop, a discussion on longevity risk in pensions schemes follows.</p><p>The forecasts performed in this study do not perfectly reflect the observed mortality change in the examined period; furthermore, the variation of the estimation errors limits the actuarial value of the projections. The findings illuminate the uncertainty that surrounds our future life expectancy as well as the difficulties associated with forecasting it.</p>

The main aim of this thesis is to analyse different mortality models regarding the longevity risk. We focus on the well-known stochastic models (Lee-Carter model, Age-period-cohort model by Renshaw and Haberman, Cairns-Blake-Dowd two-factor model) and compare them with relatively new Taiwanese model by Yang, Yue and Huang which is based on principal component analysis. Both the theoretical and also the empirical parts are included. Empirical part evaluates all the models mentioned above on the Czech mortality data from 1970-2000 for individuals aged between 50-100 years. Final mortality predictions are made for next 30 years.

Under det gångna århundradet ökade den förväntade livslängden avsevärt såväl i Sverige som i övriga världen. 1900-talets förbättrade livslängd drevs inledningsvis av en minskad barnadödlighet medan de senare årtiondena kännetecknades av minskad dödlighet i höga åldrar. En åldrande befolkning innebär ökade krav på sjukvård, äldreomsorg och inte minst pensionssystem. Pålitliga prognoser för vår framtida livslängd behövs för att beräkna de resurser som nämnda verksamheter kommer att ta i anspråk och utgör förutsättningen för en rättvis prissättning av försäkringsprodukter med levnadsrisk. Lee-Carter-modellen är en av vår tids tongivande modeller för mortalitetsprognostisering. Modellen används här för att göra livslängdsprognoser utifrån svenska mortalitetsdata; prognoserna jämförs sedan med observerade utfall. Mot bakgrund av resultatet diskuteras levnadsrisk med fokus på pensioner. Inte oväntat presterar prognoserna ingen felfri bild av verkligheten och prognosfelet varierar i storlek mellan skattningarna; att använda dem som underlag för pensionsberäkningar hade i förlängningen varit ohållbart. Exemplet illustrerar på samma gång vår osäkerhet inför framtidens livslängdsutveckling och svårigheten i att prognostisera den. / During the past century, Sweden along with many other countries experienced a sharp decline in mortality rates. The increased life expectancy was initially propelled by mortality reductions among infants and subsequently by a survival improvement in advanced ages. An ageing population has large implications for those providing services to the elderly, such as medical care and pensions, whilst also addressing the need for accurate and reliable mortality forecasts and projection methods. The Lee-Carter model is the current gold standard for mortality forecasting and has been widely adopted in several studies. Here, the model is applied on Swedish mortality data; the projections are then compared to the observed lifespan development. Against this backdrop, a discussion on longevity risk in pensions schemes follows. The forecasts performed in this study do not perfectly reflect the observed mortality change in the examined period; furthermore, the variation of the estimation errors limits the actuarial value of the projections. The findings illuminate the uncertainty that surrounds our future life expectancy as well as the difficulties associated with forecasting it.

The performance of three methods of mortality modelling and forecasting are compared. These include the basic Lee–Carter and two functional demographic models; the basic Hyndman–Ullah and the weighted Hyndman–Ullah. Using age-specific data from the Human Mortality Database of two developed countries, France and the UK (England&amp;Wales), these methods are compared; through within-sample forecasting for the years 1999-2018. The weighted Hyndman–Ullah method is adjudged superior among the three methods through a comparison of mean forecast errors and qualitative inspection per the dataset of the selected countries. The weighted HU method is then used to conduct a 32–year ahead forecast to the year 2050.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

台灣地區的人口隨著生育率及死亡率的雙重下降而呈現快速老化，其中生育率的降低影響尤為顯著。民國50年時，台灣平均每位婦女生育5.58個小孩，到了民國70年卻只生育1.67個小孩，去年（民國90年）生育率更創歷年新低，只有1.4。死亡率的下降可由平均壽命的延長看出，民國75年時男性為70.97歲，女性為75.88歲；到了民國90年，男性延長到72.75歲，女性延長到78.49歲。由於生育率的變化幅度高於死亡率，對人口結構的影響較大，因此本文分成兩個部份，主要在研究台灣地區15至49歲婦女生育率的變化趨勢，再將研究結果用於台灣地區未來人口總數及其結構的預測。 　　本研究第一部分是生育率的研究，引進Gamma函數、Gompertz函數、Lee-Carter法三種模型及單一年齡組個別估計法，以民國40年至84年（西元1951年至1995年）的資料為基礎，民國85年至89年（西元1996年至2000年）資料為檢測樣本，比較模型的優劣，尋求較適合台灣地區生育率的模型，再以最合適的模型預測民國91年至140年（西元2002年至2051年）的生育率。第二部分是人口推估，採用人口變動要素合成方法（Cohort Component Projection Method）推估台灣地區未來50年的人口總數及其結構，其中生育率採用上述最適合台灣地區的模型、死亡率則引進國外知名的Lee-Carter法及SOA法（Society of Actuaries），探討人口結構，並與人力規劃處的結果比較之。 / Both the fertility rate and mortality rate have been experiencing dramatic decreases in recent years. As a result, the population aging has become one of the major concerns in Taiwan area, and the proportion of the elderly (age 65 and over) increases promptly from 2.6% in 1965 to 8.8% in 2001. The decrease of fertility rate is especially significant. For example, the total fertility rate was 5.58 in 1961, and then decreases dramatically to 1.67 in 1981 (1.4 in 2001), a reduction of almost 70% within 20 years. 　　The goal of this paper is to study the population aging in Taiwan area, in particular, the fertility pattern. The first part of this paper is to explore the fertility models and decide which model is the most suitable based on age-fertility fertility rates in Taiwan. The models considered are Gamma function, Gompertz function, Lee-Carter method and individual group estimation. We use the data from 1951 to 1995 as pilot data and 1996 to 2000 as test data to judge which model fit well. The second part of this study is to project the Taiwan population for the next 50 years, i.e. 2002-2051. The projection method used is Cohort Component Projection method, assuming the population in Taiwan area is closed. We also compare our projection result to that by Council for Economic Planning and Development, the Executive Yuan of the Republic of China.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal