許多新興風險隨著金融市場的變化而產生，以致於發生許多大型金融災害造成許多金融產業蒙受鉅額損失。而於金融市場尋求利潤已是金融產業重要的一環，有鑑於此，本論文提出ㄧ套完整的資產配置流程，利用技術指標建構綜合信號指標作為市場指標再選擇投資資產並估計、模擬、最適化投資權重並投資，以達到規避大型金融事件風險並獲取超額利潤。本論文亦嘗試不同股票評分指標、股票資產模型、結構模型、投資組合大小等組合，以找出最適合台灣股票支股票評分指標、資產模型以及投資組合大小。 本論文發現綜合信號指標作為市場指標可有效判讀金融事件的發生與結束時間，經由此指標判斷可獲得相當的超額利潤。本論文亦發現當投資組合為5支股票、資產模型為GJR GARCH(1,1)模型、相關結構型態為多元高斯Copula時可獲得超額利潤。

abstract: A quantitative analysis of a system that has a complex reliability structure always involves considerable challenges. This dissertation mainly addresses uncertainty in- herent in complicated reliability structures that may cause unexpected and undesired results. The reliability structure uncertainty cannot be handled by the traditional relia- bility analysis tools such as Fault Tree and Reliability Block Diagram due to their deterministic Boolean logic. Therefore, I employ Bayesian network that provides a flexible modeling method for building a multivariate distribution. By representing a system reliability structure as a joint distribution, the uncertainty and correlations existing between system’s elements can effectively be modeled in a probabilistic man- ner. This dissertation focuses on analyzing system reliability for the entire system life cycle, particularly, production stage and early design stages. In production stage, the research investigates a system that is continuously mon- itored by on-board sensors. With modeling the complex reliability structure by Bayesian network integrated with various stochastic processes, I propose several methodologies that evaluate system reliability on real-time basis and optimize main- tenance schedules. In early design stages, the research aims to predict system reliability based on the current system design and to improve the design if necessary. The three main challenges in this research are: 1) the lack of field failure data, 2) the complex reliability structure and 3) how to effectively improve the design. To tackle the difficulties, I present several modeling approaches using Bayesian inference and nonparametric Bayesian network where the system is explicitly analyzed through the sensitivity analysis. In addition, this modeling approach is enhanced by incorporating a temporal dimension. However, the nonparametric Bayesian network approach generally accompanies with high computational efforts, especially, when a complex and large system is modeled. To alleviate this computational burden, I also suggest to building a surrogate model with quantile regression. In summary, this dissertation studies and explores the use of Bayesian network in analyzing complex systems. All proposed methodologies are demonstrated by case studies. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2018

Some methods for generating scenarios from multidimensional distribution assume we are able to generate scenarios from the one-dimensional distribution. We dedicate chapter 3 to this problem. At the end of the chapter, we provide references for applicable algorithms. Chapter 4 is focused on selected methods for generating scenarios from multidimensional distributions. In chapter 4.3, we introduce an algorithm for generating scenarios, which do not use any assumption about the distribution, except the first four moments and correlations to be specified. A method of generating scenarios based on approximation of multivariate normal distribution by the binomial distribution is described in chapter 4.5. Dimension reduction technique using principal components is presented in chapter 4.4. The algorithm is presented under the assumption of normal distribution. In chapter 4.6, we introduce the basics of the copula theory and a method for generating scenarios by C-vine copula. In chapter 5, we implement selected methods for generating scenarios for the estimation of daily value at risk for selected indexes and we discuss the results. Powered by TCPDF (www.tcpdf.org)

[pt] Muitos dos modelos de simulação de cenários de vazões, necessários para o planejamento e operação de setores elétricos, são construídos sob hipóteses rígidas. Isto pode restringir sua capacidade de representar dependências não-lineares e\ou distribuições não usuais. Cópulas superam estas limitações. Elas possibilitam que o comportamento marginal das variáveis seja modelado separadamente da estrutura de dependência do vetor aleatório. Além do mais, podem representar os mais diversos tipos de associações. Isto posto, esta tese apresenta 3 artigos onde modelos de cópulas são desenvolvidos visando a simulação de cenários de vazões. No primeiro artigo, propomos um modelo periódico de cópulas vine espaciais para simulação multivariada. As principais contribuições são a extensão para o caso periódico dos modelos de cópulas vine espaciais; a drástica redução do número de parâmetros; o desenvolvimento de um modelo não linear multivariado para simulação de cenários de vazões que incorpora a dependência temporal, a dependência espacial, a variação sazonal e o elevado número de usinas (alta dimensão). No segundo artigo, realizamos algumas modificações no modelo periódico espacial proposto que resultam em uma menor complexidade sem perda de performance. No terceiro artigo, propomos uma metodologia baseada em cópulas vine para modelar a dependência temporal de séries periódicas uni variadas de vazões. Dentre as contribuições destaca-se a construção de uma versão não-linear dos modelos periódicos autorregressivos (PAR(p)) onde a dependência temporal de qualquer ordem pode ser considerada; a possibilidade da incorporação de efeitos lineares e não-lineares; um modelo que não simula cenários com valores negativos; a flexibilidade para se modelar as distribuições marginais mensais. / [en] Many streamflow scenario simulation models, which are needed for the planning and operation of energy systems, are built on rigid assumptions. This may limit their ability to represent nonlinear dependencies and/or nonstandard distribution functions. Copulas overcome these drawbacks and represent a flexible tool for modeling multivariate distributions. They enable the modeling of the marginal behavior of variables separately from the dependence structure of a random vector. Moreover, they can represent any type of association. This thesis is composed of three working papers, wherein copula-based models are proposed, objectifying the simulation of streamflow scenarios. In the first working paper, a periodic spatial copula model is proposed to simulate multivariate streamflow scenarios. The main contributions include periodic extension of the spatial vine copulas; a distinct reduction in the number of parameters; and the development of a multivariate nonlinear model for streamflow scenario generation that incorporates time dependence, spatial dependence, and seasonal variation, and accounts for the dimensionality of the problem (high number of hydroelectric power plants). In the second working paper, some modifications are made to the periodic spatial model, resulting in lower complexity without the loss of performance. In the third working paper, a methodology based on the vine copula is proposed to model the temporal dependence structures in a univariate periodic streamflow time series. Among the contributions, the construction of a nonlinear version of the periodic autoregressive model (PAR(p)) is highlighted. The possibility of modeling linear and nonlinear effects and the flexibility of modeling the monthly marginal distributions are highlighted as well. This model does not simulate negative values.

This thesis attempts to evaluate the Markov Chain Monte Carlo (MCMC) methods Metropolis-Hastings (MH) and No-U-Turn Sampler (NUTS) to estimate systemic risk measures. The subject of analysis is an equity portfolio provided by a Nordic asset management firm, which is modelled using a vine copula. The evaluation considers three different crisis outcomes on a portfolio level, and the results are compared with a Monte Carlo (MC) benchmark. The MCMC samplers attempt to increase sampling efficiency by sampling from these crisis events directly, which is impossible for an MC sampler. The resulting systemic risk measures are evaluated both on the portfolio level as well as marginal level.  The results are divided. In part, the MCMC samplers proved to be efficient in terms of accepted samples, where NUTS outperformed MH. However, due to the practical implementation of the MCMC samplers and the vine copula model, the computational time required outweighed the gains in sampler efficiency - causing the MC sampler to outperform both MCMC samplers in certain settings. For NUTS, there seems to be great potential in the context of estimating systemic risk measures as it explores high-dimensional and multimodal joint distributions efficiently with low autocorrelation. It is concluded that asset management companies can benefit from both using vine copulas to model portfolio risk, as well as using MC or MCMC methods for evaluating systemic risk. However, for the MCMC samplers to be of practical relevance, it is recommended to further investigate efficient implementations of vine copulas in the context of MCMC sampling. / Detta examensarbete utvärderar Markov Chain Monte Carlo (MCMC)-metoderna No-U-Turn Sampler (NUTS) och Metropolis-Hastings (MH) vid uppskattning av systemiska riskmått. För att göra detta används en vine copula för att modellera en portfölj, baserad på empirisk data från ett nordiskt kapitalförvaltningsföretag. Metoderna utvärderas givet tre olika krishändelser och jämförs därefter med ett Monte Carlo (MC) benchmark. MCMC-metoderna försöker öka samplingseffektiviteten genom att simulera direkt från dessa krishändelser, vilket är omöjligt för en klassisk MC-metod. De resulterande systemiska riskmåtten utvärderas både på portföljnivå och på marginalnivå. Resultaten är delade. Dels visade sig MCMC-metoderna vara effektiva när det gäller accepterade samples där NUTS överträffade MH. Dock, med anledning av av den praktiska implementationen av MCMC-metoderna och vine copula modellen var beräkningstiden för hög trots effektiviteten hos metoden - vilket fick MC-metoden att överträffa de andra metoderna i givet dessa särskilda kontexter. När det kommer till att uppskatta systemiska riskmått finns det dock stor potential för NUTS eftersom metoden utforskar högdimensionella och multimodala sannolikhetsfördelningar effektivt med låg autokorrelation. Vi drar även slutsatsen att kapitalförvaltare kan dra nytta av att både använda riskmodeller baserade på vine copulas, samt använda MC- eller MCMC-metoder för att utvärdera systemisk risk. För att MCMC-metoderna ska vara av praktisk relevans rekommenderas det dock att framtida forskning görs där mer effektiva implementeringar av vine copula-baserade modeller görs i samband med MCMC-sampling.