In Taiwan area, the mortality rates at all ages have decreased since the end of World War II, and the life expectancy of people has increased from 62 in 1950's to 75 in 2000, which is an increase of 21%. The mortality improvement of the elderly (i.e. people ages 65 and over) is especially significant, which effects in the rapid population aging in Taiwan area. For example, the proportion of the elderly has increased from 6.14%in 1990 to 8.52% in 2000. On one hand, the prolonged life span for an individual means a longer period of retirement life and thus a larger retirement fund. On the other hand, a longer life for the government is equivalent to a more thorough social system for the elderly. Therefore, a reliable mortality rates projection is essential to both personal financial and social welfare planning. 　　In this study, we have two main objectives: First, we explore some frequent used models, such as Lee-Carter, multivariate regression and principal component methods. We use the data between 1950 to 1995 as the pilot data and 1996 to 2000 as the test data to judge which method has the smallest prediction error. In addition, based on computer simulation, we also evaluate the performance of the estimation methods for the Lee-Carter method. The second part (and the other objective) of this study is to explore the effect of mortality improvement on the pure premium of annuity insurance. In particular, we calculate the pure premium of the annuity under the best model acquired from the first part, and compare those under 1989 TSO and other life tables. We found that the pure premiums under current life tables are under estimated, which may cause the insolvency of insurance companies.

Insurance is built on the principle that a group of people contributes to a common pool of money which will be used to cover the costs for individuals who suffer from the insured event. In a competitive market, an insurance company will only be profitable if their pricing reflects the covered risks as good as possible. This thesis investigates the recently proposed Combined Actuarial Neural Network (CANN), a model nesting the traditional Generalised Linear Model (GLM) used in insurance pricing into a Neural Network (NN). The main idea of utilising NNs for insurance pricing is to model interactions between features that the GLM is unable to capture. The CANN model is analysed in a commercial insurance setting with respect to two research questions. The first research question, RQ 1, seeks to answer if the CANN model can outperform the underlying GLM with respect to error metrics and actuarial model evaluation tools. The second research question, RQ 2, seeks to identify existing interpretability methods that can be applied to the CANN model and also showcase how they can be applied. The results for RQ 1 show that CANN models are able to consistently outperform the GLM with respect to chosen model evaluation tools. A literature search is conducted to answer RQ 2, identifying interpretability methods that either are applicable or are possibly applicable to the CANN model. One interpretability method is also proposed in this thesis specifically for the CANN model, using model-fitted averages on two-dimensional segments of the data. Three interpretability methods from the literature search and the one proposed in this thesis are demonstrated, illustrating how these may be applied. / Försäkringar bygger på principen att en grupp människor bidrar till en gemensam summa pengar som används för att täcka kostnader för individer som råkar ut för den försäkrade händelsen. I en konkurrensutsatt marknad kommer försäkringsbolag endast vara lönsamma om deras prissättning är så bra som möjligt. Denna uppsats undersöker den nyligen föreslagna Combined Actuarial Neural Network (CANN) modellen som bygger in en Generalised Linear Model (GLM) i ett neuralt nätverk, i en praktiskt och kommersiell försäkringskontext med avseende på två forskningsfrågor. Huvudidén för en CANN modell är att fånga interaktioner mellan variabler, vilket en GLM inte automatiskt kan göra. Forskningsfråga 1 ämnar undersöka huruvida en CANN modell kan prestera bättre än en GLM med avseende på utvalda statistiska prestationsmått och modellutvärderingsverktyg som används av aktuarier. Forskningsfråga 2 ämnar identifiera några tolkningsverktyg som kan appliceras på CANN modellen samt demonstrera hur de kan användas. Resultaten för Forskningsfråga 1 visar att CANN modellen kan prestera bättre än en GLM. En literatursökning genomförs för att svara på Forskningsfråga 2, och ett antal tolkningsverktyg identifieras. Ett tolkningsverktyg föreslås också i denna uppsats specifikt för att tolka CANN modellen. Tre av tolkningsverktygen samt det utvecklade verktyget demonstreras för att visa hur de kan användas för att tolka CANN modellen.

Insurance is built on the principle that a group of people contributes to a common pool of money which will be used to cover the costs for individuals who suffer from the insured event. In a competitive market, an insurance company will only be profitable if their pricing reflects the covered risks as good as possible. This thesis investigates the recently proposed Combined Actuarial Neural Network (CANN), a model nesting the traditional Generalised Linear Model (GLM) used in insurance pricing into a Neural Network (NN). The main idea of utilising NNs for insurance pricing is to model interactions between features that the GLM is unable to capture. The CANN model is analysed in a commercial insurance setting with respect to two research questions. The first research question, RQ 1, seeks to answer if the CANN model can outperform the underlying GLM with respect to error metrics and actuarial model evaluation tools. The second research question, RQ 2, seeks to identify existing interpretability methods that can be applied to the CANN model and also showcase how they can be applied. The results for RQ 1 show that CANN models are able to consistently outperform the GLM with respect to chosen model evaluation tools. A literature search is conducted to answer RQ 2, identifying interpretability methods that either are applicable or are possibly applicable to the CANN model. One interpretability method is also proposed in this thesis specifically for the CANN model, using model-fitted averages on two-dimensional segments of the data. Three interpretability methods from the literature search and the one proposed in this thesis are demonstrated, illustrating how these may be applied. / Försäkringar bygger på principen att en grupp människor bidrar till en gemensam summa pengar som används för att täcka kostnader för individer som råkar ut för den försäkrade händelsen. I en konkurrensutsatt marknad kommer försäkringsbolag endast vara lönsamma om deras prissättning är så bra som möjligt. Denna uppsats undersöker den nyligen föreslagna Combined Actuarial Neural Network (CANN) modellen som bygger in en Generalised Linear Model (GLM) i ett neuralt nätverk, i en praktiskt och kommersiell försäkringskontext med avseende på två forskningsfrågor. Huvudidén för en CANN modell är att fånga interaktioner mellan variabler, vilket en GLM inte automatiskt kan göra. Forskningsfråga 1 ämnar undersöka huruvida en CANN modell kan prestera bättre än en GLM med avseende på utvalda statistiska prestationsmått och modellutvärderingsverktyg som används av aktuarier. Forskningsfråga 2 ämnar identifiera några tolkningsverktyg som kan appliceras på CANN modellen samt demonstrera hur de kan användas. Resultaten för Forskningsfråga 1 visar att CANN modellen kan prestera bättre än en GLM. En literatursökning genomförs för att svara på Forskningsfråga 2, och ett antal tolkningsverktyg identifieras. Ett tolkningsverktyg föreslås också i denna uppsats specifikt för att tolka CANN modellen. Tre av tolkningsverktygen samt det utvecklade verktyget demonstreras för att visa hur de kan användas för att tolka CANN modellen.

醫療技術的進步以及生活品質的提升，預計人類平均壽命將持續延長，以臺灣為例，男、女性平均壽命將從2011年的75.98歲、82.65歲，增加到2060年的82.0歲、88.0歲（資料來源：行政院經濟建設委員會2012年推估）。壽命延長意謂更長的退休生活，世界各國在21世紀均面對需求日殷的老年生活照顧，包括退休金制度以及老人醫療等，這些社會福利及保險勢必增加國家財務負擔，因此壽命是否繼續延長或存有極限成為大家關心的議題。近年來，不少研究透過死亡壓縮(Mortality Compression)連結壽命議題，亦即探討死亡年齡是否將集中至更窄的範圍，但因為資料及研究方法的限制，死亡壓縮是否成立仍無定論。 本研究以統計方法、分配假設、資料品質，三個面向來探討死亡壓縮與延壽之間的關係。本研究提出三種數值優化方法：加權最小平方法(Weighted Least Squares；WLS)、非線性極值法(Nonlinear-Maximization；NM)及最大概似估計法(Maximal Likelihood Estimation；MLE)，透過電腦模擬衡量方法優劣，與過去常見的方法比較（Kannisto的SD(M+)），探討何者具有較小的均方誤差(Mean Squared Error；MSE)。其次若死亡年齡之真實死亡分配為t分配時，探討以常態假設代入計算所產生的偏誤；最後則是套入各國實際死亡資料，使用上述較佳的估計方法，檢視死亡壓縮是否存在。 研究結果顯示，NM具有不偏性質且具有較小的均方誤差，過去研究常用的SD(M+)反而有明顯偏誤，且隨著觀察值越多變異數反而增加。而若真實死亡分配若為t分配時，以原先利用常態假設所計算的年金險保費皆有低估的情形，分配的重要性可見一斑，進而探討在實務上常態分配之假設，發現與仍與實際情形有明顯之差異，不論是NM及SD(M+)在死亡壓縮的探討下，皆受到資料的限制而有待商榷。 / Due to the advance in medical technology and the change of life style, the human life expectancy has been increasing since the end of the Second World War II and it is expected to continue the pace of increment. Longer life expectancy also means a longer life after retirement. People living in the 21st century are faced with growing demand for the retirement life, such as the pension funds and medical needs to the individuals, as well as the social welfare and insurance for the elderly to the government. Thus, the issue whether the lifespan has a limit receives a lot of attention. In particular, many studies focus on the topic of mortality compression, which means that the expectancy of lifespan has a limit and variance of lifespan converge. However, due to the availability of elderly data, there is still no consensus if the mortality compression is true. In this study, we propose estimation methods to estimate modal age and variance of the age-at-death. Three types of methods are involved: weighted least squares (WLS) method, nonlinear maximization (NM) method, and maximum likelihood estimation (MLE) method, and they are compared to the method proposed by Kannisto, namely SD(M+), in 2000. We found that the NM method has a smaller MSE, and we cannot decide the mortality compression is true based on the data from Human Mortality Database. We also applied the normality and t distribution assumption to the age-at-death and compute the pure premiums for annuity products. We found that normality distribution would produce larger premiums than using the empirical mortality rates. Similarity, the bankruptcy probability would be higher if the t distribution is used.

La recherche menée dans cette thèse propose une contribution à l’analyse du risque sur le marché de l’assurance automobile en France. Trois nouveaux axes sont présentés : le premier axe s’inscrit dans un cadre théorique de marché d’assurance automobile. Un modèle original de double asymétrie d’information est présenté. Le principal résultat qui en découle est l’existence de deux sortes de contrats d’équilibre : un contrat séparateur et un contrat mélangeant. Le deuxième point est lié à la prise en compte de la sinistralité passée dans l’étude de la relation risque - couverture. Des modèles bivariés et trivariés sont appliqués pour cette fin. Il en ressort que l’hypothèse de l’asymétrie d’information est vérifiée. Enfin, la troisième question soulevée dans cette thèse concerne l’application de la surprime aux jeunes conducteurs. Nous montrons par des modélisations économétriques de la sinistralité que la légitimité des assureurs à proposer quasi systématiquement des tarifs plus élevés aux jeunes conducteurs par rapport aux conducteurs expérimentés n'est pas toujours vérifiée. / This dissertation provides a contribution to the risk analysis on the French automobile insurance market. The objective of this thesis is threefold. The first aim relates to a theoretical framework applied on insurance market. An original model of double asymmetry of information is presented The main result that emerges is the existence of two kinds of contracts at equilibrium :a separating contract and a pooling contract. The second point concerns the past claims and the risk-coverage correlation. Bivariate and trivariate models are applied for this purpose. It results that the assumption of asymmetry of information is not rejected. The third issue is related to the over-premium that insurers apply quasi-systematically to the young drivers. We show, using econometric modeling, that this over-pricing compared to the experienced drivers’premium isnot necessary and its removal does not compromise the sustainability of the insurance company.

本次研究使用全民健康保險研究資料庫2005承保抽樣歸人檔(LHID2005)，共40萬人的承保資料，針對肺癌患者的特徵進行分析，並與美國國家癌症研究所的肺癌資料作比較，罹患肺癌的人數都呈現男性多於女性，罹癌年齡的最高峰同樣落在65歲至74歲。 接著，將門診處方及治療明細檔和住院醫療費用清單明細檔進行彙整，整理出肺癌患者在2005年至2012年之間的門診費用以及住院費用，並比較不同項目的差距及特徵，門診費用以用藥明細點數最高，住院花費前五名的項目為葯費、病房費、放射線診療費、檢查費以及治療處置費。 最後，建構肺癌治療的多重型態模型，治療方式包含手術治療、放射線治療、化學治療，估計不同狀態之間的轉換力，進而算出五年定期躉繳肺癌保單之純保費。 / This study used Longitudinal Health Insurance Database 2005 (LHID2005) from Taiwan’s National Health Insurance Research Database (NHIRD). Screening the 400,000 insured of NHIRD to select the lung and bronchus cancer patients. This study analyzed and described their characteristics. Furthermore, it compared Taiwan’s lung and bronchus cancer data with the data in the United States derived from National Cancer Institute of the USA. The results revealed that the number of male patients is more than female patients and lung cancer is most frequently diagnosed among people aged 65-74 in both countries. Another aim was to sum up the lung cancer medical cost in 2005 to 2012 from NHIRD database, including ambulatory care expenditures by visits and inpatient expenditures by admissions. The highest cost of outpatients was medicine fee. The top five inpatient expenditures were medicine fee, ward fee, radiation therapy fee, inspection fee and therapeutic treatment fee. Finally, this study constructed a multiple state model of lung cancer treatment, including surgery, radiotherapy, chemotherapy. Estimating the transition intensities from multiple state model to calculate the pure premium of a five-year lung cancer policy.