馬可夫過程是按照現在的狀態推測下一時間所發生的事件的機率模型。其中包括二大部份：一為推移機率；一為狀態空間。當時間邁進之際，其狀態就在變遷，吾人在此變動之中可做成某些結論，因馬可夫過程具有此種特性，故可分析較復雜的體系。 本文的主旨在闡明有限馬可夫過程的原理，其目的在使馬可夫過程得以靈活運用。本文內容包括有限馬可夫過程之一般理論及暫時過程的一些應用。第一章為緒論說明馬可夫過程的起源，第二章敘述馬可夫過程之一般原理及性質，第三章描述如何利用系統分析的流程圖來化簡馬可夫過程，第四章為暫時狀態在馬可夫過程所扮演的角色及暫時過程的一些應用。 生對馬可夫過程發生興趣，係受吾師鄭堯柈教授的指引與鼓勵，此恩將永誌不忘。此外周師諨星亦給生多方面指示，獲益良多，另外於師琮嘉亦多方幫忙，此文方克完成，在此均致最深切的謝意。 此門科學博大精深，以生所學之有限，寫此文，錯誤之處，勢必眾多，懇請師長，惠於指正，則幸甚矣！

本論文中，我們提出基於機場安全檢查的分層排隊理論模型，模型中的旅客基於歷史的安全數據被分成三組。我們運用二維馬可夫過程（two-dimensional Markov process）以及馬可夫調控卜瓦松過程（Markov modulated Poisson process）構建模型的排隊系統並加以分析。我們收集了台灣桃園國際機場和其它兩個機場的旅客數據以驗證我們提出的模型，並運用模擬退火法（simulated annealing）求得近似最佳解（near-optimum solution）。最後我們通過模型的旅客平均等候時間和另外兩種等候模型進行比較，之後得出我們的模型確實可以在不增加成本，甚至提升安全性的同時能夠有效地減少平均等候時間。 / This thesis proposes a tiered inspection system for airport security, wherein passengers are divided into three classes based on historical security records. A two-dimensional Markov process and a Markov modulated Poisson process (MMPP) queue were used in the formulation of the security inspection system. Simulated annealing was then used to obtain near-optimum solution for the model. The efficacy of the proposed model was evaluated using the arrival data of passengers at Taoyuan International Airport and other two international airports. A comparison with two conventional queueing models with regard to the average waiting time demonstrated the effectiveness of the proposed security inspection system in enhancing service efficiency and boosting the level of security.

Lucas(1976) 批評當時總體時間序列的計量分析方法，且主張傳統計量模型參數會隨體制及政策而改變，基於這些評論，於是許多對。嗜好(Taste)"及"技術"(Technology)" 結構參數估計的進論方法偭開始使用動態模型中的尤拉最適化條件(Euler Optimality Conditios)來進行估計。 然而，其中以Hansen(1982)所提出來的一般化動差估計法(Generalized Method of Moments)（簡稱GMM）最受矚目。此法乃源於一般化工具變數(GIVE)，在不需強烈假設下進行估計。其估計過程大致可分為下列三個階段： 1.建立正交化條件え建立目標函數最小化2.過度確認限制(overidentifying restriction) 之檢定問題因其本身即涵蓋許多估計式，如GIVE，MLE，2SLS， 且能滿足有限樣本性質，快速數斂。此法目前已用於總體計量，非線性理性預期實證及財務金融計量上。而本文應用台灣總體時間序列於資產訂價模型的GMM參數估計過程，證明了資料的適用性。另外，蒙地卡羅(Monte Carlo) 實驗設計模擬亦應用在本文研究，來探討有限樣本下的統計量之行為，並獲致適當的推論。 / Lucas(1976) criticized the existing strategies for econometricic analysis of macroeconomic time series and argues that papameters of traditional econometric models are not invariant with respect to shifts in policy regimes. In response to that criticism, several inference strategies for "taste and technology" structural parameter models using Euler optimality conditions in dynamic models were suggested. Hansen's(1982) Generalized Method of Moments(henceforth GMM) instrumental variables procedure is among the most notable inference strrategies for structural parameters. The procedure of GMM may consist three steps: (l)Set-up of the orthogonality conditions (2).Minimizing the objective function. (3)Test of the overidentifying restrictions In this paper we can understand the statistical properties of GMM estimator of Consumption-Based structural parameters obtained from Capital Asset Pricing Model by the use of Monte Carlo Simualtion .

本研究以確定給付型退休基金為對象，建構廣義隨機評價模型，以衡量不確定情況下退休基金之財務風險。希望藉著模型建構的過程，適切地描述基金評價過程中所應考量的各項要素。 為了強調基金評價時同時考量內外部精算假設的重要性，本研究將模型分為存活函數、經濟函數和給付函數三部份討論；存活函數利用離散時間非同質性半馬可夫過程（Discrete Time Non-Homogeneous semi-Markov Process）描述成員狀態轉移的機率，把成員工作年資、年齡和及狀態納入評價過程，有別於傳統僅以年齡為假設基礎之精算方法；經濟函數則以隨機過程表達外部環境的不確定性，結合上述假設資訊預估未來給付後，成為半馬可夫隨機精算評價模型，此一般性的模型能推展至基金評價時所需的各項流程。因此，本研究將模型應用於我國公務人員退撫基金，針對公務人員退撫基金的給付特性發展財務評價公式，完整地描述基金精算成本計算、未來人力與現金流量結構模擬以及敏感度分析等過程。 最後，本研究撰寫公務人員精算評價資訊系統，具體化半馬可夫隨機精算評價模型，實證公務人員退撫基金財務評價公式。實證結果也顯示，不論基金的性質或外部經濟環境，都將影響退休基金財務評價結果，為基金評價時不可忽略的精算假設。 / This study focuses on constructing a generalized valuation model for the defined benefit pension schemes. Financial soundness and funding stability are critical issues in pension fund management. In this study, a realistic stochastic model is built to monitor the uncertainty factors in affecting the financial risk and cash flow dynamics along the decision process. In order to evaluate the importance of the interior and exterior actuarial assumptions in pension valuation. Detailed models in describing the turnover patterns, economic uncertainties and benefit structures are explored. Semi-Markov process proposed by Dominicis, Manca and Granata (1991) and Janssen and Manca (1997) is extended in structuring the transition pattern of the plan’s population and the economic based factors are generated through stochastic processes. Modifications according to classification and movements of the plan member and the plan’s turnover pattern are employed to improve its practical usefulness. Then the actuarial valuations, cash flow analyses and workforce projection are performed and investigated. We has explicitly formulated the plan’s realistic phenomenon and implemented the proposed mechanism into a risk management framework for pension finance. By using this realistic approach, the cost factors could be monitored throughout the valuation. Typically these analyses involve substantial assumptions. This article has outlined the procedure of building the proposed model. Finally, Taiwan Public Employees Retirement System is simplified to illustrate the proposed methodology in pension valuation. The results from this study show that the structure of the pension schemes and the assumed economic factors are the significant factors in pension valuation. It also indicated that the fund manager can evaluate these impacts through the proposed model.