本研究以保險事業發展中心之資料分析各種不同因子如年度、性別、保額、有無體檢、保費繳別、保單年度及利差、利率等對脫退率之影響，並將其中較具顯著影響的因子納入脫退率模型之建立，期望能藉此模型準確估計台灣壽險公司生死合險、終身壽險以及定期壽險之脫退率，進而幫助壽險公司之財務規劃。 自本研究之分析發現其中最具影響力之因子為保單生效後之保單年度，因此以此為主軸建立脫退率模型，接著，亦考量利差以及利率所呈現的趨勢於其中分別建立保單年度利差模型以及保單年度利率模型，此外，更完整考量本研究中脫退率相關因素，以羅吉斯迴歸方法建立模型。最後將此四種模型應用於壽險公司準備金之提存，以生死合險為例模擬公司現金流量，發現準備金之分配如同 Tsai et al.(2002)受利率風險影響甚鉅，而加入本研究所建立之四種脫退率模型模擬後，反而減少了公司未來所須面臨的利率風險，其中又以保單年度模型影響最大，而第四種脫退率模型不同於Tsai et al.根據台灣壽險經驗加入所有具影響之因素，其模擬結果介於保單年度模型以及保單年度利率模型間，可發現考量因素之不同對脫退率影響甚鉅，繼而影響準備金之提存。 / In this article, we focus on the causes and the features of lapse rate including year, sex, size, underwriting method, premium payment mode, policy year, interest rate and interest rate difference by collecting and analyzing the empirical data of endowment, whole life insurance and term life insurance in Taiwan from Taiwan Insurance Institute. Then we take factors that have effect with lapse rate into account to establish model, and we hope to accurately estimate the lapse rate of endowment, whole life insurance and term life insurance in Taiwan by these models, and assist the life insurance companies’ financial decision making. After analyzing, we find the most effective factor of this study is the policy year, which means the year after issuing, so we take this one as our primary consideration of our lapse rate model. Then we add the interest rate difference and interest rate in the further two models. Beside this, we further consider the important factors in the part of analysis and put it in the fourth model by using Logistic Regression Model. Finally, we apply these four models to the policy reserve of life insurance company by taking endowment policy as an example simulating the cash flow. We find that the results was same as Tsai et al. (2002) that distribution of policy reserve is strongly affected by interest rate risk, but can decrease interest rate risk the company have to face in the future by adding our lapse rate models, especially the policy year model, and the fourth lapse rate model which count into most factors was not the same as Tsai et al. producing result between policy year model and the policy- interest rate model. From the results of all the lapse rate model. We can know that considering different factors in the model will bring such distinct contribution amount of reserve for life insurance company.

本論文以台灣地區人壽保險公司(國泰人壽、新光人壽、南山人壽)為對象，並且取得國泰人壽、新光人壽、南山人壽90年、91年共8季在死亡險、養老險的季資料算出國泰人壽、南山人壽、新光人壽的市場佔有率，期以電腦回圈模擬方式找出一穩定之馬可夫轉移矩陣，藉以瞭解國泰人壽、南山人壽、新光人壽在客戶忠誠度、客戶流失的移轉情形。再以92年度的第1季資料做驗證所尋找到的馬可夫移轉矩陣的準確性。本論文之研究結果可提供國泰人壽、南山人壽、新光人壽了解其保戶忠誠度的高低、保戶流失情形、新契約的流向、及保單脫退的多寡，以便三大保險公司在行銷策略中使檢討及改進。

當保險契約被發行時，保險公司必須被要求盡可能的具備承擔未來不可知的風險的能力。本文將死亡風險、利率風險、脫退風險以及流動性風險引入，並針對生死合險契約進行盈餘分析。在此以 Vasicek (1977) 所提出之隨機利率模型、根據被保險人理性行為作為基礎之脫退模型以及引入簡化後的 Longstaff、Mithal與Nies (2005)流動性風險債券價格來描述各種風險。根據上述模型假設下計算保費及準備金，遂以蒙地卡羅模擬法量化源於各種風險之盈餘。最後，本文計算保險公司之盈餘對各風險參數之敏感度分析，並計算各期破產與發生流動性問題之可能性。 / Once insurance contracts are issued, the insurers should be capable to deal with the unknown conditions in the future as possible. In this paper, we analyze the impact of mortality, interest rate, surrender and liquidity risks on the surplus of endowment contract. We model the interest rate risk by Vasicek model, the surrender rate based on the rational behavior of policyholders and introduce the discounted price of zero coupon bonds as the liquidity risk. Under such assumptions, we compute the premium and reserve, demonstrate the simulated insurance surplus, and finally exhibit the statistics of the surplus from different sources. The simulated results show the sensitivity of the surplus to the parameters of the risks. At the same time, we also show the probabilities of insolvency and illiquidity of the insurer before the maturity date of the contract due to the fluctuating surrender rate and liquidity risk resulting from the stochastic interest rate.

近年來因市場波動劇烈, 保險公司紛紛推出的「附保證投資型保單」, 給 予保戶在投資上的保證。然而, 附最低給付保證條件卻使得保險公司必須面 對更大的核保與財務風險。所以計算出附有最低保證條件商品的保費就顯 得格外地重要。 傳統附保證保單在訂價時,都是假設固定己知的脫退率,因為他們認為 脫退率的變化不會是影響保單價值的主因。但在Mary hardy 所著的《Investment Guarantees》一書中page 96 特別提到脫退風險: Withdrawals are more problematic. Withdrawals are, to some extent, related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable. 因此, 本文希望透過建立受經濟因子影響的解約率模型,來得到附保證保險 的風險價差。 本文考慮附保證滿期給付投資型商品(GMMB),並且使用 Heston (1993) 提出的財務市場模型以及參考Mercurio (1996,2001) 評價投資型保險之風 險承擔價差方法, 使用效用函數來描述保險契約雙方之風險趨避程度。同 時根據Kolkiewicz & Tan (2006) 假設受經濟因子的危險比率模型(hazard rate model), 來反映出資產的平均波動程度會影響保戶的脫退率。最後以 情境方式分別模擬5、10及15年到期的附保證最低滿期投資型保險之風險 價差。本研究推導之模型主要得出下列結果: (1) 保單期間愈長, 價差愈大。 (2) 價外賣權的價差高於價內。(3) 風險規避程度越高買賣價差越大。(4) 脫 退率受經濟影響愈深, 保單的買賣價差愈大。(5) 當保險公司所保證的價格 愈高時, 價差的影響愈大。 / With the fluctuation in the financial market in 2008, insurance company provided the consumers with equity-linked life insurances embedded guarantees. On the other hand, there are more risk in the financial literacy and underwriting performance of the insurance company. It is especially important to calculate the premium of the contract embedded investment guarantee properly . Traditional method of pricing the contract embedded investment guarantee was assumed that lapse rate was known, because product providers believed lapse rate was not a major factor to price the contract. However, Mary hardy’s ”Investment Guarantees” page 96 specifically mentions about the lapse rate risk: Withdrawls are more problematic. Withdrawals are, to some extent ,related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable. So this article will found the model of lapse rate dependent on economic factors and further get the fair value of one kind of a contract embedded guarantee: GMMB. We will build a financial model introduced by Heston (1993) and use the methodology provided by Mercurio (1996,2001) to price the risk bearing gap of a contract embedded guarantee with utility function to depict the risk averse level between investors . And we have lapse rates affected from the fluctuation of the implying asset which is the hazard rate model used by Kolkiewicz & Tan (2006). Finally, we will simulate a set of scenarios to present the Risk bearing spreads of equity-linked life insurance embedded guarantees whose term are 5、10 and 15 years. The following are the consequences I got: (1) The longer the duration, the larger the spread. (2) The spread out of money is larger than that in the money. (3) The higher the risk aversion, the larger the buy-ask spread. (4) The deeper the influence of economy on the lapse rate, the larger the buy-ask spread. (5) The higher guarantee price insurer offer, the deeper the spread affect.

本研究主要以Cox 迴歸模型為主軸，以1995年7月1日至1999年5月7日公務人員退撫基金成員:公務人員及教育人員為研究對象，分析影響基金成員各項脫退的個別變數，並量化所擇取之變數的影響，以估計各個基金成員的脫退率。同時針對現有基金成員，評估退撫基金短期現金支出並分析之。實證結果發現：藉由Cox迴歸模型之分析可知，相異的脫退因素，被不同的迴歸變數所影響著，且各個變數對各項脫退的影響程度亦存在著差異。短期現金支出的評估結果顯示，各項給付支出，以退休給付的支出佔最大的比例，次為資遣、死亡及離職給付。而人數比例較少的教育人員，其脫退給付支出金額，高於公務人員之給付支出。 略 / Cox regression model is proposed in this study to investigate the demographic factors (i.e., gender, age, seniority, salary scale and the entry date) that influence the turnover pattern of the plan members. This research has focused on the government employees and public school teachers in Taiwan Public Employees Retirement System (Tai-PERS). Quantitative analyses on turnover are performed through monitoring and selecting the significant factors in Cox regression model. Finally based on the current members in Tai-PERS, the short-term cash outflow is projected. Based on the empirical results, different causes of turnover (i.e., death, withdrawal, layoff and retirernent) are influenced by the selected factors. Significant differences have been found within the various causes of decrements. Result from the short-term cash outflow shows that the payment due to retirement has the largest proportion. Then follows the payment amount due to payoff, death and withdrawal if we rank them in order. In additions, the total payments of the public school teachers are larger than those of the government employees, while the plan members of the public school teachers are comparatively less.

本文針對附保證年金型投資商品進行評價，其中被保險人脫退因素除受到死亡解約因素之外，對經濟環境影響因素產生解約問題，如利率攀升、經濟成長率、失業率等亦須考慮。附保證年金型投資商品公帄價值為保險公司販賣投資型年金商品須對負債面進行評價，以確保被保險人之權益，保險商品價值除因投資市場環境變動造成投資商品價值累積變動之外，對於被保險人因應市場環境轉變造成脫退問題亦影響保險公司對於投資型商品準備金價值評估，本篇依照Kolkiewicz & Tan(2006)之研究，假設附保證年金型投資商品評價方式，除投資標的受到市場變動影響外，對於經濟環境變動造成被保險人解約狀況亦考慮於核保模型中，因脫退因素考慮層面過廣，故本篇主要以死亡、經濟環境變動劇烈與利率上升導致解約因素為主要考慮狀態。 本研究推導之模型主要得出下列結果：(1)附保證年金型商品的公帄價格以保險年期的影響最大，其次為風險性資本市場長期帄均波動，而死亡率影響附保證投資年金型商品主要由風險性資本市場價值決定。(2)契約初始為主要解約期間，當解約力持續增加至一定值，契約後期解約率將趨於帄坦，本研究推估契約前期經濟市場波動易造成被保險人解約狀況，故解約程度增加。(3)主要投資型商品風險價差問題影響因素為長期市場波動程度，因風險價差之衡量主要考慮風險因子變動因素導致與公帄價值或期初保費差距，依照模型假設變動因子以風險性資產價值波動程度影響最巨，其次為保險期間，因此歸納出風險價差因子主要變動來源為風險性資產價值。 / In this paper, the goal is to evaluate fair value of guaranteed annuity-type investment products. In addition to death factors, the insured terminate by other reasons, such as interest rates raising, economic growth rate, and unemployment rate. Accordance with the liabilities side, the reserve of guaranteed annuity-type investment products must match it’s fair value. There is a question how to accurately evaluate fair value of guaranteed annuity-type investment products. The price of guaranteed annuity-type investment products is affected by two parts. One is cumulative index price change in value of investment goods, the other one is withdrawal rates. Kolkiewicz & Tan’s research assume guaranteed annuity-type investment products evaluation methods which is affected by market environment and termination status of the insured. The results show that (1) The major impact on fair value of guaranteed annuity-type investment products is mainly from the period of the insurance contracts. The secondary effect is long-term average risk capital market volatility. (2) The main terminate time is the beginning of the contracts. When the lapse rates continued to increase to a certain value, lapse rate tends to smooth.(3) The major impact on risk spread of guaranteed annuity-type investment products is mainly from long-term market volatility. To sum up, the major changes in sources of risk spreads factor are from asset value.