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In this paper I apply the Rational Actor model to the 1993-1994 North Korean Nuclear Crisis. I begin with two hypotheses: 1) North Korea attempted nuclear armament because of its perception of threat from South Korea and the United States; 2) North Korea attempted nuclear armament because it wanted to use its nuclear program as leverage to obtain economic assistance from the United States. I conduct a diplomatic historical analysis based on the Rational Actor model to determine which was North Korea's primary objective, and conclude that the primary objective of North Korea was obtaining economic concessions, but that threat perception did seem to play a role in the decision to start the nuclear program. In this process, I show that the Rational Actor model was insufficient in the analysis and that it must be complemented by cultural factors, "thickening" the rationality. / Master of Arts

Life insurance companies rely on mortality rate models to set appropriate premiums for their services. Over the past century, average life expectancy has increased and continues to do so, necessitating more accurate models. Two commonly used models are the Gompertz-Makeham law of mortality and the Lee-Carter model. The Gompertz-Makeham model depends solely on an age variable, while the Lee-Carter model incorporates a time-varying aspect which accounts for the increase in life expectancy over time. This paper constructs both models using training data acquired from Skandia Mutual Life Insurance Company and compares them to validation data from the same set. The study suggests that the Lee-Carter model may be able to offer some improvements compared to the Gompertz-Makeham law of mortality in terms of predicting future mortality rates. However, due to a lack of qualitative data, creating a competitive Lee-Carter model through Singular Value Decomposition, SVD, proved to be problematic. Switching from the current Gompertz-Makeham model to the Lee-Carter model should, therefore, be explored further when more high quality data becomes available.

臺灣的男女死亡率皆呈現逐年遞減的趨勢，自1993年進入高齡化社會後，預計將會在2018年進入高齡社會；人口不斷老化的結果讓社會上不論人民或是如保險公司等年金提供者皆面臨愈來愈嚴重的長壽風險；目前現有文獻提出了許多方式以解決長壽風險，其中多數的方法皆需使用到對未來死亡率之預估。 本研究為了能夠更準確的預估未來死亡率的趨勢，參考了Lee Carter (1992)所提出之模型以及Li and Lee (2005)、Li (2013)提出之共同改善趨勢效果，提出考慮商品與商品間以及商品與整體人口間共同改善趨勢之死亡率模型；本研究利用臺灣之保險公司壽險及年金業務經驗死亡率和Human Mortality Database之臺灣人口資料對模型進行配適，並以MAE、MAPE、RMSE三項指標比較與Lee Carter模型之優劣。 最後，本研究利用所配適之模型進行預測，模擬自然避險之效果，檢視臺灣保險業進行自然避險的可能效益，並對決策者在於決定是否要進行自然避險方面給出建議。 / Taiwan became an aging society in 1993 and is expected to become an aged society in 2018. The progressive decrease in Taiwan mortality since the 20th century for both genders has made longevity risk a serious problem for both people and annuity provider in Taiwan. So far, the literature has discussed about how to deal with longevity risk and came out with several solutions which can be categorize as “industry self-insurance”, “ mortality projection improvement” and “capital market solutions” , most of them are related to the projection of mortality. In order to provide a more precise projection of future mortality trend, this article designs several models which collaborates Lee Carter Model (1992) and the common improvement trend suggested by Li and Lee (2005). Based on our models, the Taiwan insurance industry experience mortality data and the Taiwan population mortality data, we test the performance of our models and make comparison. Lastly, we use the model we find to project future mortality trend and try to make a simulation of natural hedging strategy in Taiwan. The purpose we do this is to test the performance of natural hedging method and give suggestion for the decision-maker when they are considering whether to execute a natural hedging strategy.

台灣地區居民近年的死亡率下降速度加快，使得我國國民的平均壽命在公元2000年已超過美國，成為長壽的國家之一。其中我國國民死亡率的下降幅度因年齡而不同，且各個年代、世代也不相同，與APC（Age-Period-Cohort）模型採年齡、年代與世代三個因子分析死亡率頗為一致，因此本文計畫以APC模型研究台灣的死亡率。然而，由於「年代＝年齡＋世代」之線性相關，參數估計值有甄別問題（Identification Problem），使得參數估計值不唯一。 文獻中有不同方法解決APC模型的參數估計問題，近年又有Fu（2000）提出之本質估計量（Intrinsic Estimator），可直接解決參數估計及其變異數。因此本文首先以電腦模擬驗證本質估計量，以及過去其他估計方法，檢測這些方法是否可得出理論的結果。本文的第二部分則以西元1961至2005年的資料探討APC模型的實用性，分析APC與Lee-Carter模型的優劣；研究發現APC模型用於估計死亡率時，整體而言雖不如Lee-Carter模型，但可彌補Lee-Carter模型在高年齡有較大誤差的不足，唯在年輕族群則仍有改善空間，未來或可考慮APC與Lee-Carter模型的結合。 / The mortality rates in Taiwan area have been experiencing dramatic decreases in recent years. The life expectancy has surpassed that in the United States in 2000 and Taiwan has become one of the longevity countries. Besides, the falling of mortality rates varies in different age, period, and cohort groups, which corresponds to the APC (Age-Period-Cohort) model. Therefore, the goal of this paper is to study the mortality rates in Taiwan area with APC model. However, due to the linear dependency of age, period and cohort (Period = Age + Cohort), there is the identification problem, that is, the parameter estimates are not unique. A number of solutions to the identification problem in APC model have been provided in the literature. Fu (2000) introduce a new estimator, the Intrinsic Estimator (IE), which can solve parameter estimates and variance directly. In the first part of this research, computer simulation is conducted to examine the IE, compared with other methodologies. In the second part of this research, data from 1961 to 2005 are used for verifying the validity of APC model in fitting mortality rates, and we analyze the strengths and weaknesses between the APC and Lee-Carter model. The results from our study indicate that the APC model in estimating mortality rates does not show as well as the Lee-Carter model as a whole. However, the APC model performs better than the Lee-Carter model for the elderly mortality rates, but is still needed to be improved in young groups. In the future, it can be considered to combine the APC and Lee-Carter model.

本研究主要分為三個部分：第一個部分探討壽險公司保單組合之最適資產配置；第二個部分探討確定提撥退休金制度下，員工所面臨的資產配置問題；第三個部分則為方法論的比較研究。此外，本文也探討長命風險(longevity risk)等相關議題。本文在Huang與Cairns (2006) 所提出的資產報酬模型下，推導出累積資產價值的期望值以及變異數，並利用套裝軟體的最佳化程式(optimization programming)獲得給定目標函數下的最適投資策略。 在保單組合資產配置之研究方面，我們分別針對保險公司繼續經營的商品以及即將停賣的商品提出合適的資產配置方式。常數資產配置方式(Constant rebalance rule)適合持續經營的商品，變動資產配置方式(Variable rebalance rule)則適合即將停賣的商品。在常數資產配置方式下，我們能夠得到投資組合的效率前緣線。此外，不管是何種資產配置方式，當保單組合的保單到期日較近時，保險公司必須增加其所持有的現金比例。 在確定提撥制下最適資產配置問題的研究方面，本文的結果符合一般退休基金經理人所採取的生命週期型態投資方式。本研究發現在Lee-Carter模型之下，考慮時間加權可以增加模型的預測能力。而在考慮長命風險下，員工必須採取更積極的投資策略。 本文決定資產配置之方法為預期模型(Anticipative model)，其在評價日時即決定未來的決策，不考慮新訊息對決策的影響。考慮新訊息會對決策產生影響的決定資產配置方法為適應模型(Adaptive model)。在第五章的研究裡，我們比較上述兩種決定資產配置方法之差異。研究結果發現，若以期望值與標準差為判斷標準，兩種決定資產配置方法並沒有絕對的優劣關係。而若在每個決策執行的時間點重新使用預期模型來決定新的資產配置策略，則其所對應的投資策略以及投資績效會與適應模型下的策略與投資績效接近。因此，在無法獲得適應模型投資策略封閉解的情況下，預期模型投資策略可以有效的近似適應模型投資策略。 / The purpose of this thesis is to investigate the asset allocation issue of the long-term investors. Our approach is to calculate theoretical formulae of the first two moments of the accumulated fund; we then adopt optimization programming to find a asset allocation strategy that fits the fund management target. Two kinds of investors are explored. The first one is an investment manager who manages a general portfolio of life insurance policies, and the second one is an employee who starts his career life in a DC pension plan. We also survey the longevity risk issue in this thesis. In the study of “optimal asset allocation for a general portfolio of life insurance policies”, two kinds of rebalancing methodologies are examined. For constant rebalance rule, which is applicable to a continuing business line, we find an efficient frontier in the mean-standard deviation plot that occurs with arbitrary policy portfolios. Also, the insurance company should hold more cash to reduce its illiquidity risk for portfolios in which policies will mature at earlier dates. In the study of “optimal asset allocation incorporating longevity risk in defined contribution pension plans”, we confirm the suitability of the lifestyle investment strategy. Investors in a DC pension plan should be more aggressive when he considers the longevity risk. Furthermore, we proposed a time adjustment technique to capture mortality predictions more precisely in this study. The approach of decision making of this thesis is referred to anticipative model, which does not consider the possible feedback from the future information. On the other hand, the approach of decision making that consider the possible feedback from the future information is referred to adaptive model. We further compare the two approached in the study “Comparative efficiency- anticipative model versus adaptive model”. The numerical results show that investors would not prefer the adaptive approach to the anticipative approach in the mean-variance criterion. Moreover, the downside risk is larger when the strategy is decided by adaptive approach. We also find that the strategy and its numerical distribution of anticipative approach can approximate to that of adapted approach if one re-assesses it at every decision date. Thus, the anticipative approach provides a first approximation on looking for the optimal investment strategy of adaptive model.

臺灣婦女生育率下降快速，近年來屢創新低，堪稱全球生育率最低的國家，總生育率自民國89年1.68、降為民國98年1.03，民國99年甚至降至0.90以下，提升生育率成為政府施政的重要課題。因為資料限制，生育率大多以總生育率(Total Fertility Rate)表示，而非較能反映婦女一生生育總數的世代完成生育率(Completed Cohort Fertility Rate)。這兩者間存有不少差異，以生育率下降的臺灣為例，總生育率會因生育時機遞延而低估世代生育率，以總生育率詮釋生育率可能有瑕疵。有鑒於此，本文以比較「世代」及「年代」兩者的差異，以生育率及死亡率為研究對象，探討較適宜描述臺灣特性的模型。 由於世代生育率會有資料不足的問題，本文使用外推法(Extrapolation)補足年齡較高（如35歲以上）的婦女生育率，並以四種模型估計年代生育率與世代生育率，包括Gamma模型、Gompertz模型、主成份分析(Principle Component Analysis)與單一年齡組個別估計法，希望找出適合預測臺灣世代完成生育率的模型。除了台灣資料，也用日本、法國與美國的世代生育率資料，比較各國世代生育率模型的異同。另外，本文也以世代及年代兩種觀點，類似生育率的探討方式，比較常用死亡率模型的優劣。 不論是生育率或是死亡率資料，配適模型結果皆以世代資料可得到較好的估計結果，生育率以單一年齡組個別估計法為最佳的模型，死亡率則以Gamma模型、主成份分析、單一年齡組個別估計法為較佳的模型。 / Taiwan’s fertility rates have been declining radically in recent years, much faster than most countries in the world. For example, the total fertility rate (TFR) is 1.68 in 2000, 1.03 in 2009, and even reduces to 0.90 in 2010. Therefore, one of the top priorities for Taiwan government policies is to enhance the willingness of having children. Due to the data availability, the TFR is used more often, although the completed cohort fertility rate (CFR) is a more reasonable measurement. However, previous studies showed that the TFR is likely to be influenced by the deferring (i.e., tempo effect) of childbearing and produces misleading results. In order to measure the effect of deferring childbearing, this study focuses on exploring the difference of measures in the view of cohort and period (especially the CFR vs. TFR) and evaluates which fertility and mortality model is more appropriate for Taiwan. Because there are fewer complete cohort fertility data, we use extrapolation to make up the higher age-group fertility data (such as aged 35 and above). We consider four fertility models in this study, including Gamma model, Gompertz model, principal component analysis, and individual group estimation. We use the data from Taiwan, Japan, France and United State data to evaluate these fertility models. The results indicate that the parametric models (Gamma and Gompertz) have the worst performance, probably due to the rapid change of fertility behaviors. In addition, similar to evaluating the fertility models, we compare the performance of frequently used mortality models using the cohort and period mortality data. The result shows that using cohort data to estimate fertility and mortality is better than period data. Also individual group estimation is the best model to fit fertility; the better models to fit mortality are Gamma model, principle component analysis and individual group estimation.