本研究旨在探討金融危機期間，美國與歐洲金融市場之日內報酬率、實質波動度、連續波動度與跳躍風險行為之日內因果關係，並採用美國三大指數期貨(S&P 500, Dow Jones, Nasdaq)及歐洲期數期貨(FTSE, DAX, CAC)之高頻資料，檢定是否具有顯著槓桿效果(Leverage Effect)與波動度回饋效果(Volatility Effect)、在報酬率與跳躍風險之間具有相互影響效果。探討在金融危機發生前、後期間其日內報酬率、實質波動度、連續波動度與跳躍項間在1分鐘、5分鐘及60分鐘之抽樣頻率下之日內行為。因此，實證研究包含金融市場之上升及下降趨勢，顯示在金融危機發生後，日內波動度與跳躍項之槓桿效果(Leverage Effect)與波動度回饋效果(Volatility Effect)受到叢聚(Clustering)現象影響且顯著增加。不同抽樣頻率下之因果關係效果在金融危機發生前、中、後期間，特別在5分鐘及60分鐘之抽樣頻率方式，跳躍風險受到波動度回饋效果影響呈顯著增加，此實證結果對政策制定者及投資人具有重要之意涵。 / This study examines the intraday causality between returns, volatility and jumps in the U.S. and European markets during the financial crisis. examine whether during the financial crisis, the S&P 500, Dow Jones, Nasdaq, FTSE, DAX and CAC index futures markets have a significant impact on the leverage and volatility feedback effects, as well as whether these interactions also occur between returns and jumps. The intraday behavior of 1-min, 5-min and 60-min sampling of returns, volatility and jumps is examined by employing data from the period between financial crisis. The study covers the major upward and downward trends in the market. Our empirical data indicate the main leverage and volatility feedback effects caused by intraday volatility and jump clustering significantly increased after the financial crisis. The causality effects with different sampling frequencies before, during and after the financial crisis show that jumps have increased the volatility feedback effect, especially when in a 5-min and 60-min sampling frequency is used. These findings have important implications for both policymakers and investors.

本研究顯著地發展時間轉換Lévy過程在最適投資組合的運用性。在連續Lévy過程模型設定下，槓桿效果直接地產生跨期波動度不對稱避險需求，而波動度回饋效果則透過槓桿效果間接地發生影響。另外，關於無窮跳躍Lévy過程模型設定部分，槓桿效果仍扮演重要的影響角色，而波動度回饋效果僅在短期投資決策中發生作用。最後，在本研究所提出之一般化隨機波動度不對稱資產報酬動態模型下，得出在無窮跳躍的資產動態模型設定下，擴散項仍為重要的決定項。 / This study significantly extends the applicability of time-changed Lévy processes to the portfolio optimization. The leverage effect directly induces the intertemporal asymmetric volatility hedging demand, while the volatility feedback effect exerts a minor influence via the leverage effect under the pure-continuous time-changed Lévy process. Furthermore, the leverage effect still plays a major role while the volatility feedback effect just works over the short-term investment horizon under the infinite-jump Lévy process. Based on the proposed general stochastic asymmetric volatility asset return model, we conclude that the diffusion term is an essential determinant of financial modeling for index dynamics given infinite-activity jump structure.

Modern medical practice and science involve complex phenotypic definitions. Understanding patterns of association across this range of phenotypes requires co-analysis of high-dimensional association studies in order to characterise shared and distinct elements. In this thesis I address several problems in this area, with a general linking aim of making more efficient use of available data. The main application of these methods is in the analysis of genome-wide association studies (GWAS) and similar studies. Firstly, I developed methodology for a Bayesian conditional false discovery rate (cFDR) for levering GWAS results using summary statistics from a related disease. I extended an existing method to enable a shared control design, increasing power and applicability, and developed an approximate bound on false-discovery rate (FDR) for the procedure. Using the new method I identified several new variant-disease associations. I then developed a second application of shared control design in the context of study replication, enabling improvement in power at the cost of changing the spectrum of sensitivity to systematic errors in study cohorts. This has application in studies on rare diseases or in between-case analyses. I then developed a method for partially characterising heterogeneity within a disease by modelling the bivariate distribution of case-control and within-case effect sizes. Using an adaptation of a likelihood-ratio test, this allows an assessment to be made of whether disease heterogeneity corresponds to differences in disease pathology. I applied this method to a range of simulated and real datasets, enabling insight into the cause of heterogeneity in autoantibody positivity in type 1 diabetes (T1D). Finally, I investigated the relation of subtypes of juvenile idiopathic arthritis (JIA) to adult diseases, using modified genetic risk scores and linear discriminants in a penalised regression framework. The contribution of this thesis is in a range of methodological developments in the analysis of high-dimensional association study comparison. Methods such as these will have wide application in the analysis of GWAS and similar areas, particularly in the development of stratified medicine.