以往利用貝氏方法估計卜瓦松均數，為了計算的可行性，大多用伽碼分配（卜瓦松的共軛分配）當成均數的先驗分配，且先驗分配以經驗貝氏法來估計（母數經驗貝氏法），然而在卜瓦松均數背離伽碼分配的狀況下，估計效果並不佳。Laird (1978)提出無母數最大概似先驗分配估計法，提供卜瓦松均數之先驗分配另一選擇。當均數不具伽碼分配而集中在某些值時，此法有很好的估計效果;但在均數分散（變異數大）的狀況下，估計效果並不理想。由於在大多數的情況下，我們無法確定均數分配的型式，因此無從判定用何種估計方法較為妥當。本文首先嘗試用Escobar (1994)所提出的Dirichlet過程估計法來估計卜瓦松均數，並由模擬結果得知，不論均數之型態為伽碼分配或少數幾個值的離散分配，Dirichlet過程估計法的效果總是介於無母數最大概似估計法及母數經驗貝氏法之間，並趨向其中較好的估計法。 / In the past, when using the Bayesian method to estimate Poisson means, we used to choose conjugate prior distribution for computational simplicity, and we also empirically estimated the prior of the means Gamma distribution (PEB). However, if the true distribution of the means departs from Gamma distribution, PEB method is not very efficient. Laird (1978) estimated the prior distribution by nonparametric maximum likelihood (NPML), which provided another choice of the prior distribution. When the means are clustered in few values instead of having Gamma distribution, NPML method is very efficient, but when the means are very disperse, the method is not efficient. Because, most of the time, we do not know the true distribution of the means, it is hard to decide whether to use PEB or NPML method. This research first try to estimate Poisson means by Dirichlet Process (DP) method which is developed by Escobar (1994). According to our simulation study, whether the distribution of the means is Gamma distribution or discrete distribution having few values, DP method is as good as PEB method when PEB method is better than NPML method, and it is as good as NPML method when NPML method is better.

本文包含關於估計風險與動態資產配置的兩篇研究。第一篇研究主要就當須估計的投資組合其投入參數具有高維度特質的觀點下，探究因忽略不確定性通膨而對資產配置過程中帶來的估計風險。此研究基於多重群組架構下所發展出的新投資決策法則，能夠確實地評價不確定性通膨對資產報酬的影響性，並在應用於建構大規模投資組合時，能有效減少進行最適化投資決策過程中所需的演算時間與成本。而將此模型應用於建構全球ETFs投資組合的實證結果則進一步顯示，若在均值變異數架構下，因建構大型投資組合時須估計高維度投入參數而伴隨有大量估計風險時，參數估計方式建議結合採用貝氏估計方法來估算資產報酬的一階與二階動差，其所對應得到的投資組合樣本外績效會比直接採用歷史樣本動差來得佳。此實證結果亦隱含：在均值變異數架構下，穩定的參數估計值比起最新且即時的參數估計資訊對於投資組合的績效來得有益。同時，若當投入參數的樣本估計值波動很大時，增加放空限制亦能有利投組樣本外績效。 第二篇文章則主要處理當處於對數常態證券市場下時，投資組合報酬率不具有有限動差並導致無法在均值變異數架構下發展出最適化封閉解時的難題。本研究示範此時可透過漸近方法的應用，有效發展出在具有放空限制下，考量了估計風險後的簡單投資組合配置法則，並且展示如何將其應用至實務上的資產配置過程以建構全球投資組合。本文的數值範例與實證模擬結果皆顯示，估計風險的存在對於最適投資組合的選擇有實質的影響，無估計風險下得出的最適投資組合，不必然是存有估計風險下的最適投資組合。此外，實證模擬結果亦證明，當存有估計風險時，本文所發展的簡單法則，能使建構出的投資組合具有較佳的樣本外績效表現。 / This dissertation consists of two essays on dynamic asset allocation with regard to dealing with estimation risk as being in different uncertainties in the mean-variance framework. The first essay concerns estimation errors from disregarding uncertain inflation in terms of the need in estimating high-dimensional input parameters for portfolio optimization. This study presents simplified and valid criteria referred to as the EGP-IMG model based on the multi-group framework to be capable of pricing inflation risk in a world of uncertainty. Empirical studies shows the proposed model indeed provides a smart way in picking worldwide ETFs that serves well to reduce the amount of costs and time in constructing a global portfolio when facing a large number of investment products. The effect of Bayesian estimation on improving estimation risk as the decision maker is subject to history sample moments for input parameters estimations is meanwhile examined. The results indicate portfolios implementing the Stein estimation and shrinkage estimators offer better performance compared with those applying the history sample estimators. It implicitly demonstrates that yielding stable estimates for means and covariances is more critical in the MV framework than getting the newest up-to-date parameters estimates for improving portfolio performance. Though short-sales constraints intuitively should hurt, they do practically contribute to uplift portfolio performance as being subject to volatile estimates of returns moments. The second essay undertakes the difficulty that the probability distribution of a portfolio's returns may not have finite moments in a lognormal-securities market, and thus leads to the arduous problem in solving the closed-form solutions for the optimal portfolio under the mean-variance framework. As being in a lognormal-securities market, this study systematically delivers a simple rule in optimization with regard to the presence of estimation risk. The simple rule is derived accordingly by means of asymptotic properties when short sales are not allowed. The consequently numerical example specifies the detailed procedures and shows that the optimal portfolio with estimation risk is not equivalent to that ignoring the existence of estimation risk. In addition, the portfolio performance based on the proposed simple rule is examined to present a better out-of-sample portfolio performance relative to the benchmarks.

針對金融時序資料變異數不齊一的性質，隨機波動模型除了提供於ARCH族外的另一選擇；且由於其設定隱含波動本身亦為一個隨機波動函數，藉由設定隨時間改變且自我相關的條件變異數，使得隨機波動模型較ARCH族來得有彈性且符合實際。傳統上處理隨機波動模型的參數估計往往需要面對到複雜的多維積分，此問題可藉由貝氏分析裡的馬可夫鏈蒙地卡羅法解決。本文主要的探討標的，即在於利用馬可夫鏈蒙地卡羅法估計美元/新台幣匯率隨機波動模型參數。除原始模型之外，模型的擴充分為三部分：其一為隱含波動的二階自我回歸模型；其二則為藉由基本模型的修改，檢測匯率市場上的槓桿效果；最後，我們嘗試藉由加入scale mixture的方式以驗證金融時序資料中常見的厚尾分配。

偵測新興議題對於研究者而言是一個相當重要的問題，研究者如何在有限的時間和資源下探討同一領域內的新興議題將比解決已經成熟的議題帶來較大的貢獻和影響力。本研究將致力於協助研究者偵測新興且具有未來潛力的研究議題，並且從學術論文中探究對於研究者在做研究中有幫助的學術智慧。在搜尋可能具有研究潛力的議題時，我們假設具有研究潛力的議題將會由同一領域中較具有影響力的作者和刊物發表出，因此本研究使用貝式估計的方法去推估同一領域中相關的研究者和學術刊物對於該領域的影響力，進而藉由這些資訊可以找出未來具有潛力的新興候選議題。此外就我們所知的議題偵測文獻中對於認定一個議題是否已經趨於成熟或者是否新穎且具有研究的潛力仍然缺乏有效及普遍使用的衡量工具，因此本研究試圖去發展有效的衡量工具以評估議題就本身的發展生命週期是否仍然具有繼續投入的學術價值。 本研究從許多重要的資料庫中挑選了和資料探勘和資訊檢索相關的論文並且驗證這些在會議論文中所涵蓋的議題將會領導後續幾年期刊論文相似的議題。此外本研究也使用了一些已經存在的演算法並且結合這些演算法發展一個檢測的流程幫助研究者去偵測學術論文中的領導趨勢並發掘學術智慧。本研究使用貝式估計的方法試圖從已經發表的資訊和被引用的資訊來建構估計作者和刊物的影響力的事前機率與概似函數，並且計算出同一領域重要的作者和刊物的影響力，當這些作者和刊物的論文發表時將會相對的具有被觀察的價值，進而檢定這些新興候選議題是否會成為新興議題。而找出的重要研究議題雖然已經縮小探索的範圍，但是仍然有可能是發展成熟的議題使得具有影響力的作者和刊物都必須討論，因此需要評估議題未來潛力的指標或工具。然而目前文獻中對於評估議題成熟的方法僅著重在議題的出現頻率而忽視了議題的新穎度也是重要的指標，另一方面也有只為了找出新議題並沒有顧及這個議題是否具有未來的潛力。更重要的是單一的使用出現頻率的曲線只能在議題已經成熟之後才能確定這是一個重要的議題，使得這種方法成為落後的指標。 本研究試圖提出解決這些困境的指標進而發展成衡量新興議題潛力的方法。這些指標包含了新穎度指標、發表量指標和偵測點指標，藉由這些指標和曲線可以在新興議題的偵測中提供更多前導性的資訊幫助研究者去建構各自領域中新興議題的偵測標準。偵測點所代表的意義並非這個議題開始新興的正確日期，它代表了這個議題在自己發展的生命週期上最具有研究的潛力和價值的時間點，因此偵測點會根據後來的蓬勃發展而在時間上產生遞延的結果，這表示我們的指標可以偵測出議題生命力的延續。相對於傳統的次數分配曲線可以看出議題的崛起和衰退，本研究的發表量指標更能以生命週期的概念去看出議題在各個時間點的發展潛力。本研究希望從這些過程中所發現的學術智慧可以幫助研究者建構各自領域的議題偵測標準，節省大量人力與時間於探究新興議題。本研究所提出的新方法不僅可以解決影響因子這個指標的缺點，此外還可以使用作者和刊物的影響力去針對一個尚未累積任何索引次數的論文進行潛力偵測，解決Google 學術搜尋目前總是在論文已經被很多檢索之後才能確定論文重要性的缺點，學者總是希望能夠領先發現重要的議題或論文。然而，我們以議題為導向的檢索方法相信可以更確實的滿足研究者在搜尋議題或論文上的需求。 / This research presents endeavors that seek to identify the emerging topics for researchers and pinpoint research intelligence via academic papers. It is intended to reveal the connection between topics investigated by conference papers and journal papers which can help the research decrease the plenty of time and effort to detect all the academic papers. In order to detect the emerging research topics the study uses the Bayesian estimation approach to estimate the impact of the authors and publications may have on a topic and to discover candidate emerging topics by the combination of the impact authors and publications. Finally the research also develops the measurement tools which could assess the research potential of these topics to find the emerging topics. This research selected huge of papers in data mining and information retrieval from well-known databases and showed that the topics covered by conference papers in a year often leads to similar topics covered by journal papers in the subsequent year and vice versa. This study also uses some existing algorithms and combination of these algorithms to propose a new detective procedure for the researchers to detect the new trend and get the academic intelligence from conferences and journals. The research uses the Bayesian estimation approach and citation analysis methods to construct the prior distribution and likelihood function of the authors and publications in a topic. Because the topics published by these authors and publications will get more attention and valuable than others. Researchers can assess the potential of these candidate emerging topics. Although the topics we recommend decrease the range of the searching space, these topics may so popular that even all of the impact authors and publications discuss it. The measurement tools or indices are need. But the current methods only focus on the frequency of subjects, and ignore the novelty of subjects which is critical and beyond the frequency study or only focus one of them and without considering the potential of the topics. Some of them only use the curve of published frequency will make the index as a backward one. This research tackles the inadequacy to propose a set of new indices of novelty for emerging topic detection. They are the novelty index (NI) and the published volume index (PVI). These indices are then utilized to determine the detection point (DP) of emerging topics. The detection point (DP) is not the real time which the topic starts to be emerging, but it represents the topic have the highest potential no matter in novelty or hotness for research in its life cycle. Different from the absolute frequent method which can really find the exact emerging period of the topic, the PVI uses the accumulative relative frequency and tries to detect the research potential timing of its life cycle. Following the detection points, the intersection decides the worthiness of a new topic. Readers following the algorithms presented this thesis will be able to decide the novelty and life span of an emerging topic in their field. The novel methods we proposed can improve the limitations of impact factor proposed by ISI. Besides, it uses the impact power of the authors and the publication in a topic to measure the impact power of a paper before it really has been an impact paper can solve the limitations of Google scholar’s approach. We suggest that the topic oriented thinking of our methods can really help the researchers to solve their problems of searching the valuable topics.