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.

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.