自從民國七十一年起惡性腫瘤（俗稱癌症）開始躍昇為國人十大死因之第一位，而且癌症死亡率有逐年攀升的趨勢。另外，根據衛生署公佈的「民國八十五年癌症登記報告」中，發現國人罹患癌症的情況不僅有集中特定癌症而且亦有逐年遞增的現象，由此可知癌症一直威脅著國人的健康。 由於政府在民國八十四年開辦全民健康保險，提供大部份國民基本的醫療保障，然而健保的給付項目以及金額仍然有限，因此壽險業者為了補足全民健保的缺口，陸續推出終身癌症保險以提供國人更完整的保障。然而國內終身癌症保險仍屬初期階段，缺乏完整的統計經驗資料，大部份採用國外再保險公司所提供的癌症經驗資料，並未參酌國內醫院所作的癌症統計；壽險業最近因損失率過高，也將終身癌症保險的給付內容重新修訂，以作為調整保費的依據，因此其終身癌症保險之保費適足性值得探討。 本研究限定在定額型個人終身癌症保險，主要探討在國人癌症發生率逐年上升情況下，如何去建立一套終身癌症保險費率釐定模型，並且參考國內醫院的癌症統計資料，在合理的精算假設下，使用S-Plus統計軟體計算出終身癌症保險之保費，進一步探討壽險業之費率適足性。 在本文實證分析中，列舉國內三家壽險公司，就其給付內容比較保費，並探討其保費適足性，發現其相同處在於國內三家壽險公司的年繳保費明顯不足，而且其年繳保費差額隨著年齡呈直線遞增。其兩者年繳保費之比率方面，本實證分析的年繳保費皆高出三家壽險公司二至四倍左右，因此在長期之下保費的不足會導致壽險公司虧損，進而可能影響到壽險公司的清償能力，此結果可提供壽險業者及監理機關參考。 / With the increasing of cancer incidence rate, the insurers provide completely and thoughtfully designed planning in order to meet the requirements of the public, supplemental to the national health insurance program enforced by the government of R.O.C. in 1995. However, many domestic insurers have faced the problem of the experience loss ratio beyond the expected. Since the whole life cancer insurance policies have been issued on the market a few years ago, the empirical data from the insurance are insufficient for the pricing. In addition, only a fewer researches have focused on the actuarial model of this type of insurance. In this paper, we will investigate the premium calculation of the whole life cancer insurance under the influence of specified factors, and outline the appropriate model construction procedures. The data we use are not only from Department of Health of the Executive Yuan but also from domestic hospital, such as National Taiwan University Hospital and Veterans General Hospital. Moreover, we make reference to medical studies and make use of rational actuarial assumptions, i.e., the trend of cancer incidence rate, cancer survival rate, cancer outpatient rate, average cancer outpatient treatment days, cancer inpatient rate, cancer surgical rates, cancer radiotherapy or chemotherapy rates, average cancer radiotherapy or chemotherapy treatment days, cancer bone marrow transplantation rates, cancer mortality rates, and other cancer rates, available to the premium calculation in empirical analysis. Finally, we examine the premiums of three whole life insurance policies to compare to our results in empirical analysis and discuss whether premiums are adequate. We hope that this paper could be beneficial to the actuaries and also provide suggestions for the government surveillance.

台灣腎臟病問題嚴重，不論是洗腎發生率或盛行率，在2008年均高居世界首位。許多討論認為一個主因在於民眾聽信地下電台買藥，因濫服來路不明成藥導致腎臟功能衰竭，連帶造成健保洗腎醫療費用節節高升，於2008年達到318億，成為健保中花費最高單一治療項目。 本論文主要目在釐清地下電台是否造成洗腎發生率和盛行率增加。由於地下電台普遍設於中南部且絕大多數以閩南話播放，這些節目對於外省籍榮民影響相對有限。本論文使用國衛院發行的健保資料承保檔與重大傷病檔，採DDD模型(difference-in-difference-in-difference)，比較同一地域但不同承保人口 (農民、榮民，與地區人口) 中，五十五歲以上洗腎發生率和盛行率是否因投保人口而有明顯差異，藉以釐清地下電台對腎臟病影響。估計結果顯示在2000年後高高屏地區農民洗腎發生率有略高於榮民，而雲嘉南地區農民和榮民的洗腎發生率不存在明顯差別。

犯罪，是人類社會一直存在的問題。近年來，隨著社會結構的變遷、都市化發展程度快速、人口密度集中及大量人口流動性的影響，人民的生活環境與居住空間亦愈趨複雜，加上政局動盪經濟衰退，失業人口節節上升，社會價值觀的變化，使得臺灣地區的犯罪問題層出不窮，社會治安亦因此受到影響。犯罪案件的發生不僅對社會整體治安產生影響，亦對人民的生命財產安全及生活品質構成威脅。因此，犯罪的嚴重程度與治安良窳實為地方民眾與警政機關最為關切之問題。 為了適切反映臺灣地區之犯罪現象與治安狀況，本研究應用集群分析方法，以內政部警政署所公佈的臺灣地區2010年各地區之「警政統計資料」為主，藉由實證研究以了解各行政地區之犯罪狀況與警察機關之破案績效。其中，犯罪嚴重程度之衡量指標分別以各刑案之犯罪發生次數及發生率作為評估準則，而警察機關之偵查破案績效則以破獲率作為評核基準。分別依照發生數與破獲率、發生率與破獲率之分群結果，建構治安狀況之分級指標，以了解我國主要之刑案犯罪於臺灣各地區的犯罪嚴重程度與其破案績效。 研究結果顯示，在發生數與破獲率方面，高雄市在各種犯罪類型中皆被歸為發生數最高且破獲率最低的集群，新北市與臺北市次之，而大多數的縣市被歸類於治安較佳的集群之中。分局部分以高雄市-鳳山分局被歸為各種犯罪類型中發生數最高且破獲率最低的集群，臺北市大安分局、中山分局次之。而臺中市-東勢分局、高雄市-鹽埕分局、高雄市-六龜分局、臺中市-和平分局則屬於各種犯罪類型中發生數最低且破案率最高的集群。 在發生率與破獲率方面，高雄市在各種犯罪類型中皆被歸為發生率最高且破獲率最低的集群，花蓮縣次之，而臺東縣、金門縣、連江縣被歸類為發生率較低且破獲率較高的集群。分局部分以臺北市-中正第一分局、高雄市-新興分局被歸為各種犯罪類型中發生率最高的集群，且其破案績效亦為最低，惟暴力犯罪之破獲率表現較佳之外，其餘方面都有待改善。

運用傳統再保險契約移轉風險受限於承保能量的逐年波動，尤其自90年代起，全球巨災頻繁，保險人損失巨幅增加，承保能量急遽萎縮，基於巨災市場之資金需求，再保險轉向資本市場，預期將巨災風險移轉至投資人，促成保險衍生性金融商品之創新，本研究針對佔有顯著交易量的巨災風險債券進行分析，基於Cummins和Geman (1995)所建構巨災累積損失模型，引用Duffie 與Singleton (1999)於違約債券的計價模式，將折現利率表示為短期利率加上事故發生率及預期損失比例之乘積，並將債券期間延長至多年期，以符合市場承保的需求，應用市場無套利假設及平賭測度計價的方法計算合理的市場價值，巨災損失過程將分成損失發展期與損失確定期，以卜瓦松過程表示巨災發生頻率，並利用台灣巨災經驗資料建立合適之損失幅度模型，最後以蒙地卡羅方法針對三種不同型態的巨災風險債券試算合理價值，並具體結論所得的數值結果與後續之研究建議。 / Using traditional reinsurance treaties to transfer insurance risks are restrained due to the volatility of the underwriting capacity annually. Catastrophe risks have substantially increased since the early 1990s and have directly resulted significant claim losses for the insurers. Hence the insurers are pursuing the financial capacities from the capital market. Transferring the catastrophe risks to the investor have stimulated the financial innovation for the insurance industry. In this study, pricing issues for the heavily traded catastrophe risk bonds (CAT-bond) are investigated. The aggregated catastrophe loss model in Cummins and Geman (1995) are adopted. While the financial techniques in valuing the defaultable bonds in Duffie and Singleton (1999) are employed to determine the fair prices incorporating the claim hazard rates and the loss severity. The duration of the CAT-bonds is extended from single year to multiple years in order to meet the demand from the reinsurance market. Non- arbitrage theory and martingale measures are employed to determine their fair market values. The contract term of the CAT-bonds is divided into the loss period and the development period. The frequency of the catastrophe risk is modeled through the Poisson process. Taiwan catastrophe loss experiences are examined to build the plausible loss severity model. Three distant types of CAT-bonds are analyzed through Monte Carlo method for illustrations. This paper concludes with remarks regarding some pricing issues of CAT-bonds.

近年來，隨著我國國民的壽命持續增長，人口老化愈加明顯。預期臺灣在2021年將進入人口零成長，2025年65歲以上人口比例也將超過20%（來源：國家發展委員會2014年人口推估）。人口老化帶來許多問題，如老年生活、醫療、以及長期照顧等需求，其中照顧需求與年齡正相關，預期需求將隨壽命延長而增加，需要及早規劃及因應，這也是今年通過長期照護法的原因。由於各國國情不同，對於長期照護的定義、補助及需求也不盡相同，有必要發展適用於臺灣特性的，推估長期照顧需求的所需之資源。重大傷病中的許多疾病與失能、甚至長期照護有關，由於全民健保實施至今已逾20年，重大傷病的認定標準及程序相對客觀、中立，受到民眾、學術、政府各界肯定。 有鑑於此，本文以全民健保資料庫的重大傷病資料庫為基礎，挑選八類引發長照的重大傷病，作為規劃長期照護保險的參考。本文以這些傷病的發生率、罹病後死亡率、罹病後存活率等，結合國發會所人口推估的結果，利用年輪組成法(Cohort Component Method)推估長期照顧的未來需求。研究發現：未來需求人口從2013年約10萬人，迅速增加至2060年的21萬人，增加速度相當快。而參考「長期照顧保險法」草案的給付內容，若聘請一名外籍看護每月20,000元計算，每人分擔將從2012年的$530元/月升至2060年的2,728元/月；若不調整保費且以隨收隨付計算，每人每月繳交400元長照保費，長照給付將從2012年每月13,353元降至2060年每月3,556元，由此可知壽命延長、人口老化將造成長照保險的財務問題。另外，本文考量的八項重大傷病較為保守，沒有加入老化、遺傳等因素的長照需求，預期將不足以因應實際需求，未來有必要引入商業保險來彌補社會保險的不足。 / In recent years, with the sustainable growth of the life expectancy in our country, population aging becomes more apparent. Taiwan’s population of ages 65 and over will exceed 20% within 10 years, before 2025. (Source: National Development Council - Population Projection on 2014). The population aging an prolonging life incurs a big demand for caring the elderly, such as the economic need after the retirement, medical cost, and long-term care. Among these needs, the demand of long term care was under-estimated and is only recognized recently. Thus, this study focuses on predicting the need of long-term care in Taiwan. Specifically, the definition and standard (as well as types and amounts of subsidy) for juding whether one needs long-terma care is not yet determined, although Taiwan’s government passed the long-term care law (Long-Term Care Insurance Law) earlier this year. We should adapt the notion of catastrophic illness (CI) and use certain CI categories, which are related to long-term care, to design the long-term care insurance. Catastrophic illness (CI) is one of the key features of Taiwan’s National Health Insurance (NHI), and the definition and process of evaluating if one is with the CI is quite complete. We choose eight categories of CI and use the NHI database to obtain their incidence rates, mortality rates, and survival probability. Together with the population projection from National Development Council in 2014 and the cohort component method to predict the long-term care demand in Taiwan. The syudy result shows that the population needing long-term care will rise from about 100 thousands in 2013 to about 210 thousands in 2060. Moreover, if the long-term care insurance is funded via pay-as-you-go, the individual premium required will rise 5 times from 2012 to 2060. This indicates that the long-term care might be too expensive and the commercial insurance can play an important role as a supplement.

再發事件資料常見於醫學、工業、財經、社會等等領域中，對再發資料分析研究時，我們往往無法確知再發事件發生的時間或是發生次數的分配。因此，本論文探討的是分析再發事件的無母數方法，包括Nelson提出的平均累積函數(mean cumulative function)估計量，及Wang、Chiang與Huang介紹的發生率(occurrence rate)之核函數(kernel function)估計量。 就平均累積函數估計量來說，藉由Nelson導出的變異數及自然(naive)變異數，可分別求得平均累積函數的區間估計。本文利用靴環法(bootstrap)計算出平均累積函數在不同時點的變異數，再與Nelson變異數及自然變異數比較，結果顯示Nelson變異數與靴環法算出的變異數較接近。因此，應依據Nelson變異數建構出事件發生累積次數之漸近信賴區間。 本論文亦介紹了兩個或多個母體的平均累積函數的比較方法，包含固定時點之比較與整條曲線之比較。在固定時點之下，比較方法分別為平均累積函數成對差異之漸近信賴區間及靴環信賴區間、變異數分析比較法，與排列檢定法；而整條曲線比較方法包含：類似 統計量、Lawless-Nadeau檢定。這些方法應用在本論文所採之實證資料時，所得到的檢定結論是一致的。 / Recurrent event data arise in many fields, such as medicine, industry, economics, social sciences and so on. When studying recurrent event data, we usually don’t know the exact joint or marginal distributions of the occurrence times or the number of events over time. So, in this article we talk about some nonparametric methods, such as the mean cumulative function (MCF) discussed by Nelson, and kernel estimation of the rate function introduced by Wang, Chiang and Huang. As to the estimator of MCF, we can compute the confidence interval by Nelson’s variance and naive variance. We use bootstrap method to compare the performance of Nelson variance of the estimated MCF and naive variance of the estimated MCF. The results show that Nelson variance is better than naive variance, so we should construct the confidence limits for the MCF by Nelson’s variance except when only grouped data are available. We also introduce methods for comparing MCFs, including pointwise comparison of MCFs and comparison of entire MCFs. Methods for pointwise comparing MCFs include approximate confidence limits for difference between two MCFs, analysis-of-variance comparison, permutation test, and bootstrap’s confidence limits for difference between two MCFs. Methods for comparing entire MCFs include a statistic like Hoetelling’s , and Lawless-Nadeau test. Finally, all approaches are employed to analyze a real data, and the conclusions concordance with each other.