The number of insurance company has grown rapidly in Taiwan due to insurance deregulation since 1992. The main challenge insurance industry face is the declination of profit due to the increasing of competitors. The operator of insurance company is able to face this question and offer the solution, then a company has better solvency. So we explore two issue, one is to investigate the relationship between asset risk and capital adjustment decision in Taiwan¡¦s life insurance industry from 1993 to 2005, and the other is to provide some empirical evidences of retention limit of excess of loss reinsurance in Taiwan¡¦s property insurance industry. In the first issue, a life insurance company is in less risk and has better solvency when it has more capital or higher ratio of capital; however, this also brings higher opportunity cost which means in long run, the average profit will be lower. There is no conclusion how to balance the relationship between capital adjustment and risk taking decision in life insurance industry though this topic is intensively discussed these days. Therefore, with the methodology of panel data threshold regression, we divide life insurance companies into two categories according to ¡§life insurance and annuity insurance premiums to total premiums ratio¡¨. One is life insurance Company of indemnification, and the other is the one of savings. In conclusion, we identify the negative correlation between capital ratio and risk of life insurance company of indemnification and the positive correlation between capital ratio and risk of life insurance company of savings. In the second issue, because of the increase of natural disaster in Taiwan recently, the property insurance company has to face what the reinsurance companies are not willing to underwriter, so excess of loss reinsurance has become the viable solution in Taiwan¡¦s property insurance industry. We apply extreme value theory to the tail of Taiwan property insurance claim for VaR estimation and calculate retention limit of excess of loss reinsurance. The empirical results show that the distribution of Taiwan property insurance claim is fat-tailed. We suggested using Generalized Pareto Distribution (GPD) to model the data with extreme loss and conclude retention limit of excess of loss reinsurance.

Reinsurance is one of the most important tools to be used by insurance companies, for managing risks. This is an effective way / however, there are situations where reinsurance is insufficient, such as the occurrence of a natural hazard. When a natural hazard occurs, many insured experience loss at the same time, which drains the reinsurance market capacity. If future market capacity could be forecasted, then it would be easier for companies to decide when to include cat bonds or any other additional securities in their portfolio. In order to establish a model for market capacity, its relationship with other market parameters and the association among parameters are examined. In this study, these relationships are analyzed and used to establish an algorithm for predicting the next years reinsurance capacity. Moreover, last 10-year data for market capacity is used to establish and AR(1) model, in order to create a comparison with the algorithm. A case study of cat bonds is done, which uses the pricing load calculation of the Lane model and aims to ease the decision-making process by comparing the loads of cat bond and reinsurance pricing.

Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.

Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.

本研究之主要貢獻為發展適合台灣營造綜合險保單（本體損失險）之風險曲線。 先前由Salzmann (1963)及Ludwig (1998)之相關研究，係採用美國市場之損失經驗，考量不同保單之承保範圍、不同保險標的、及不同之承保風險，直接引用美國市場風險曲線於台灣市場之通用性值得釐清。 本研究回顧台灣營造綜合險保單之承保範圍及除外條款，依據西元一九九六年至兩千年之損失經驗，發現台灣營造綜合險之損率深受天然災害如地震、颱風、豪雨所影響。 再保險安排可分成兩大類，一是比例再保險; 另一是非比例再保險。風險曲線是非比例再保險常用之計價方式之一。 比較先前之研究，本研究之風險曲線分佈集中在低層其主要之原因如下:- 一、 分析標的之可能最大損失(PML)偏低: PML代表某一特定危險所可能造成之可能最大損失。以道路工程為例，其可能最大損失小於30%之保額。由於道路工程大多綿延數十公里甚或更長，其工程本身呈線狀之分佈。換言之，非常不可能會有單一損失其損失金額超過保額之30%。 因此，道路工程之損失分佈不平均且分佈集中在低層。 二、 營造綜合險保期偏長: 營造工程其中一個特性為多年期的保險期間。 因為工程之進行往往需要花超過一年的時間來完成，因此，營造綜合險全損(損失金額等於保額)之機率，遠小於財產險因火災造成全損之機率。 三、 分析之承保風險不同: Salzmann (1963)僅針對火災此一危險因子來從事她的研究。就我們所知，美國大多數住宅皆是木造，屬可燃性建材，火災造成之影響相當大。 相反地，本研究標的大多利用不可燃性建材來興建，如鋼鐵或混凝土，故火災之影響性相對較小。 關鍵字: 非比例再保險、風險基礎計價、營造綜合保險 / The major contribution of this research is to develop the exposure curves suitable for the Taiwan Contractor’s All Risks (CAR) Insurance (Material Damage Cover). The exposure curves generated in Salzmann (1963) and Ludwig (1998) were originated from the loss experience in the United States. Considering the different types of policies, different types of risks, and different types of perils, the applicability of those curves in Taiwan market is discussable. This study reviews the scope of coverage, insuring clause and exclusions of the Taiwan Contractor’s All Risks Insurance. According to the loss records between 1996 and 2000, it’s understood that the result of the Contractor’s All Risks Insurance is highly influenced by the natural catastrophic perils, such as earthquake, typhoon and heavy rains. The reinsurance placement can be categorized into proportional and non-proportional reinsurance or called excess of loss reinsurance. Exposure rating is one of the common pricing methods for the excess of loss reinsurance. Compared with those two previous researches done by Salzmann (1963) and Ludwig (1998), the outcome of this analysis shows an unbalanced loss distribution which leans to the lower layers that is mainly because of the following reasons: - (1) Low PML percentage of analyzed risks: The PML represents the Probable Maximum Loss subject to a certain type of peril. Taking a road construction project as an example, the PML of a road construction project is less than 30% of the total sum insured. Usually, the length of a road construction project is tens of kilometers or even much longer. In consideration of its linear shape, it’s very unlikely to have a loss exceeding 30% of its total sum insured. Therefore there was very few or nil loss data above the 30% of the total sum insured that’s the reason why the loss distribution is unbalanced and leans to the lower layers. (2) Long Construction Period of a CAR Project: A character of a CAR project is having a multiple-year policy period because the construction work usually takes more than one year to be completed. Therefore the possibility to have a total loss case, loss amount equal to the total sum insured, is much less than a property risk with a fire scenario. (3) Types of Perils Analyzed: Salzmann (1963) carried out her research by analyzing the peril of fire covered under the homeowners’ policies. As we know, most of the houses in the United States are the wooden structures, which are combustible. Oppositely, the risks in this research are mostly constructed by using the non-combustible materials, such as steel or reinforced concrete. Keywords: excess of loss, non-proportional reinsurance, exposure rating, and contractor’s all risks insurance.

國內保險經營，長久以來即是人身保險及財產保險分業經營方式，但兩者的經營規模差距很大，據統計資料顯示，壽險業這五年來的傷害險保費收入，平均每年約有580億元，健康險平均年約1260億元，對於產險業整體業界總保費收入約1100億元的市場規模而言，實在是塊誘人和商機無限的新市場，能加入傷害險或健康險的經營，將是產險業者突破經營瓶頸的關鍵，不僅保險市場會產生蛻變，更會對消費大眾帶來多元的選擇與影響。 在此背景下，本研究主要探討產險業經營傷害險的績效，並舉個案實例經營此單一險種的過程，就其在商品研發、行銷、核保和理賠等各項作業流程，進行探討分析。經本研究個案分析，歸納出幾點問題，一是在經營策略面，以業績成長為首要的考量，自然會選擇通路商的行銷方式，所謂「掌握通路，就是贏家」，兩年來通路業績佔了該險種的73%，而其賠款金額佔率，亦佔了76%左右，經營績效的結果顯示出「成也通路，敗也通路」，如何強化通路商之管理是經營重點。二是由理賠資料分析統計，並與壽險業資料比較，發現有相關性趨勢，但卻有相對惡化的現象，諸如平均死亡率，男性比女性多出5倍以上，比壽險業的3倍高；平均每件死亡賠款230萬元，比壽險業的120萬元，高出近一倍，且又以男性50~59歲的年齡層最高，此點顯示出其商品是否有「保費太低而保障過高」的問題。三是其面臨人力和經驗不足的問題，加上缺乏醫療、法務、徵信調查等相關專業人員及其運作經驗，無法在核保和理賠作業時，因應實際的作業需求。 我國保險法經過兩次修正後，現在已開放產險業者得以經營傷害險，再者，有關健康險是否可進一步開放予產險業者經營，相信很快會經立法院通過修法審議。故本研究的結果，即是找出經營問題和原因，並提出改善建議，期能提供產險業者經營傷害險或未來健康險的參酌。 關鍵字：個人傷害保險、綜合率、非比率再保險 / In our insurance market, there are two types of operation, that is, life insurance and non-life insurance, but the business scale of the two types has a long way to go. According to the data, the average premium income of whole life insurance market of the personal accident and health insurance is about NT$58 billion and NT$126 billion per year respectively among these five years. Relative to the non-life insurance which premium income is about NT$110 billion, it’s really a captivating and unlimited new market that the non-life insurance can take the risk about the personal accident and health insurance. From my point of view, it will be the main key to break through the bottleneck of operation of the non-life insurance market. Not only the whole insurance market will be changed but also it can bring multi-choice and influence to consumers. Under this background, the main task of this research is discussing the non-life insurance’s result of operation the personal accident insurance. It has a real case that also includes the product of development, marketing, underwriter and claim for further discussion and analysis. According to the research of this case, it can generalize some points as below. The first is about the tactic of operation: we will choice the way of marketing way of channel if we consider the growth of premium income as primary issue. What is called” Someone will be a winner if he controls the channel”. In our company, the business of channel was occupied about 73% of the personal accident insurance and the claim also in the same situation was about 76% over the past two years. Unfortunately, the result of operation is “Control the channel will make someone success and failure”, so the key point of operation is how to enhance the management of channel. The second is about the statistics of claim: we compared with the data of life and non-life insurance and find some related trends, but there is a phenomenon of related aggravation, such as rate of average death, men are five times more than women in non-life insurance but only three times in life insurance statistics; the average indemnity of death is about NT$2.3 million in non-life insurance which is one time higher than life insurance market and especially with men that age level among in 50~59 years old. On the basis of above mentioned, it shows the problem of this product have higher indemnification but lower premium income. The third is about the problem of lack of manpower and inadequate experience, in addition, it also lack such relevant professional personnel as medical, legal and investigative, etc. So it can’t offer the demand of real operation in the underwriting and claim process. The law of insurance has already opened that the non-life insurance can operate the personal accident insurance after revision two times in our country. Moreover, we believe that will be passed through about the non-life insurance also can operate the health insurance by the legislative rapidly. After the analysis, the conclusion of this research is finding out the question and reason of operation and offering the suggestion of improvement. I hope it can provide some recommendations for the non-life insurance that will operate the personal accident insurance or oncoming of the health insurance. Key words: Personal Accident Insurance、Combined Ratio、Excess of Loss

Probably the most frequently used definition of reinsurance is insurance for insurance companies, by reinsurance the cedant (insurance company) cedes part of the risk to the reinsurer. Reinsurance plays nowadays a crucial role in insurance industry as it does not only reduce the reinsured's exposure, but it can also significantly reduce the required solvency capital. In past few decades various approaches to reinsurance actuarial modelling were published and many actuaries are nowadays just reinsurance specialized. The thesis provides an overview of the actuarial aspects of modelling a non-life per risk and for motor third party liability per event excess of loss reinsurance structure, according to the author's knowledge no study of such wide scope exists and various aspects have to be found in various fragmented articles published worldwide. The thesis is based on recent industry literature describing latest trends and methodologies used, the theory is compared with the praxis as the author has working experience from underwriting at CEE reinsurer and actuarial reinsurance modelling at global reinsurance broker. The sequence of topics which are dealt corresponds to sequence of the steps taken by actuary modelling reinsurance and each step is discussed in detail. Starting with data preparation and besides loss inflation, more individual claims development methods are introduced and own probabilistic model is constructed. Further, burning cost analysis and probabilistic rating focused on heavy tailed distributions are discussed. A special attention is given to exposure rating which is not commonly known discipline among actuaries outside of reinsurance industry and different methodologies for property and casualty exposure modelling are introduced including many best practice suggestions. All main approaches to the reinsurance modelling are also illustrated on either real or realistically looking data, similar to those provided by European insurance companies to their reinsurers during renewal periods.

近年來許多的產險公司因為買不到比例性的天災再保險合約，不得不使用超額賠款再保險方式以規避和轉嫁天災風險，但也因此承擔相當大的天災累積風險。 本文將企業風險管理的概念引進，把保險公司的再保部門模擬成企業的風險管理部門，期能更精確地定位保險公司再保險部門的功能、應該扮演的角色及未來經營策略。 超額賠款再保險之使用與產物保險的經營關聯密切，其最重要關鍵在於風險自行承擔，因此其間的保費收入、再保費成本支出等有關費率釐定計算方式，可說是超額賠款再保險之精華所在，亦為保險相關從業人員必備之專業知識。由於超額賠款再保險運用到許多統計相關的計算說明，本文之論述期能幫助保險相關從業人員找到各方的均衡點，有助於保險事業將資源做最有效率、效能的經營。 本文針對財產保險運用超額賠款再保險經營實務之考量加以介紹，同時強調經營者必須提升專業，包括損防服務、專業化核保、作業流程電腦化、財務風險管理等，尤其在計算天災的累積和購買適當再保險的承保容量方面，這亦有助於保險公司對天災風險的評估與認識。 最後，本文籲請保險公司主管必須重視目前以超額賠款再保險風險自留方式所承保之業務其費率是否適當，尤其是天災風險，所謂多算勝，少算不勝，而況於無算乎？否則會和賭場的賭客一樣， 大部分人是輸光退場的。 / Excess of Loss Reinsurance has become the viable solution in Taiwan’s insurance community, since the constraints were imposed by reinsrers a few years ago that natural catastrophe exposures could not be fully transferred to proportional treaties. But, the insurers also take very large natural risks at the same time. The aforementioned is the key issue to be discussed at the first part of this text, which introduces the concept of “corporate risk management” that Risk Management Department in enterprise is playing a role very similar to Reinsurance Department in an insurance company. We can, from this perspective, easier and clearer identify the functions and business objectives of Reinsurance Department in an insurance company. One distinctive advantage over proportional reinsurance is that, by adopting XOL reinsurance, ceding companies can expect to retain more premiums. Virtually, the performance of XOL operations is directly linked to the level of reinsurance cost, so it is very vital for insurance people to be fully aware of the connections between their insured exposures and reinsurance prices. A number of charts, tables, and cases are illustrated in the text for the calculation of XOL prices, and readers, particularly those who are doing insurance business, of this text are able to fairly locate the equilibrium of reinsurance cost that can be mutually accepted by the insured、brokers、reinsurers and insurers. Actual practices of applying property XOL reinsurance are analyzed in the text, which has also highlighted the importance of upgrading insurers’ professionalism, including loss prevention, underwriting, work-flow computerization, financial risk management, in particular, aggregate control on natural perils and adequate reinsurance protection. My conclusions and recommendations are pinpointing the issues required to be dealt with by the authorities for the adequacy of direct premium rates, particularly for the business with natural perils that are retained under XOL programs. Insurers are destined to be out of the market, sooner or later, if they are unable to charge sufficient premiums to finance their losses in the long run.

決定自留額是保險人承接業務時之主要考量因素，以發揮保險之基本原理原則：危險分散與損失分攤。自留額釐定不當，不僅影響保險人財務結構，甚至波及公司整體核保營運成果而危及清償能力。本文選擇某產險公司實際損失分配資料，探討不同自留比例與再保方式對營運結果之影響，結果顯示在此實際損失分配資料模型下，適度調高自留比例，應可增加核保利潤。本文進一步以相關性分析探討自留配置。 / Retention is a key element for the insurer to determine how much it wishes to retain for its own account for the risks it has written. This point is fundamental to carrying on the business of insurance and akin to the principle upon which insurance is based, namely the spreading of risks and sharing of losses. The risk of incurring a retained loss owning to inadequate retention, which would imperil financial objective even can affect the overall underwriting results and arise insolvency. This paper select data base of occurred loss distribution for the past three years to study the impact of different retained ratio and different type of reinsurance for performance. This paper shows that, the underwriting profit can be expected to increase when the retention increases precisely under the existing loss distribution model . This paper also discuss the related factors in deciding retention by correlation analysis.

過去台灣的地震保險一直受到忽略，因此缺乏完整的地震損失資料。本研究主要的目的是利用統計方法來模擬地震損失，估計地震損失所造成的直接損失金額，並且進一步討論如何控制地震超額損失保險的預期損失。 本研究推論災害性地震發生頻率是一個負二項分配﹔而損失幅度則利用所求出的房屋倒塌數模型，再假設每一棟倒塌房屋的個設價格作加總而得，因此模擬出地震損失，可以估計出預期地震損失，並且可以進一步建立地震損失機率分布情況。 對於控制地震超額損失保險的預期損失，本研究提出以理賠上限與理賠起始點兩種方式來作損失控制。實證結果發現，利用理賠上限作超額再保險會比較可以控制地震損失。同時也可以利用模擬出的結果來決定應該如何設立理賠上限與理賠起始點。 / The earthquake insurance in Taiwan is ignored for many years, so that the data of earthquake is lacked. This study applied the statistical methods to simulate the earthquake losses in Taiwan, and estimated the loss amount, and discussed how to control the expected loss of excess-of-loss insurance. The frequency of disaster earthquake is a negative binomial distribution. And the severity of each disaster earthquake is to sum up the assumed dollar amount of each damaged houses. Compounding the frequency of earthquake with the severity of earthquake, we can simulate the losses of earthquake. Hence the expected earthquake losses and the probability density function of earthquake losses are built. In order to control the expected loss of excess-of-loss reinsurance, this study compared the results of the trigger level and the capped level of the reinsurance claim, and concluded that the capped level is better than trigger level in controlling the expected loss of excess-of-loss insurance.