An optimal dividend problem with investment opportunities, taking into consideration a source of strategic risk is being considered, as well as the effect of market frictions on the decision process of the financial entities. It concerns the problem of determining an optimal control of the dividend under debt constraints and investment opportunities in an economy with business cycles. It is assumed that the company is to be allowed to accept or reject investment opportunities arriving at random times with random sizes, by changing its outstanding indebtedness, which would impact its capital structure and risk profile. This work mainly focuses on the strategic risk faced by the companies; and, in particular, it focuses on the manager's problem of setting appropriate priorities to deploy the limited resources available. This component is taken into account by introducing frictions in the capital structure modification process. The problem is formulated as a bi-dimensional singular control problem under regime switching in presence of jumps. An explicit condition is obtained in order to ensure that the value function is finite. A viscosity solution approach is used to get qualitative descriptions of the solution. Moreover, a lending scheme for a system of interconnected banks with probabilistic constraints of failure is being considered. The problem arises from the fact that financial institutions cannot possibly carry enough capital to withstand counterparty failures or systemic risk. In such situations, the central bank or the government becomes effectively the risk manager of last resort or, in extreme cases, the lender of last resort. If, on the one hand, the health of the whole financial system depends on government intervention, on the other hand, guaranteeing a high probability of salvage may result in increasing the moral hazard of the banks in the financial network. A closed form solution for an optimal control problem related to interbank lending schemes has been derived, subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to real bank networks by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network. Finally, a possible computation technique for the Default Risk Charge under to regulatory risk measurement processes is being considered. We focus on the Default Risk Charge measure as an effective alternative to the Incremental Risk Charge one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets emitted by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible, because of both new regulation and the high speed - low cost technology available nowadays.

鑒於近年全球海外可轉換公司債發行檔數大增，然而以此商品為研究主題的文獻並不多，於是決定以此為研究目標。 　　影響海外可轉換公司債的價格因素包括股票價格、匯率、國內利率、國外利率和發行公司的違約機率，因此可買回、可賣回海外可轉換公司債是一個複雜的商品，而評價也較為困難。本文採用三維度二項樹和最小平方蒙地卡羅法建立評價海外可轉債的數值模型。為了更貼近真實世界，本文考量各變數間相關性和動態信用風險；另外，為了使評價更為精準，於股價過程中加入跳躍過程。 　　本文將模型運用至兩檔台灣公司所發行的海外可轉債，發現理論價格傾向於高估，但是理論價格與市價極為接近，尤其當以最小平方蒙地卡羅法評價時。另外本文也針對發行條件和模型中各個變數作敏感度分析，其中重要的是發現股票波動度、股票與匯率間相關係數在海外可轉債評價中扮演重要的角色。 / The number of Euro-convertible bonds issued has highly increased in the early 2010s. However, the related literature is barely found. This paper studies the pricing models of this investment product. Euro-convertible bonds are complex instruments affected by the credit risk of the issuers, the dynamic process of stock prices, the term structure of the interest rate and the movement of the exchange rate in the same time. Accordingly, building the ECB pricing model is a hard work. This paper presents a model considering the dynamic credit risk and jump in stock price process to make valuation more precise. Another advantage of models in this paper is use of stochastic interest rates for both local and foreign so as to make the model more staying with the real world. The other advantage is taking the correlation between each random variables into account. For pricing the Euro-convertible bonds, the numerical methodologies used in this paper are three-dimension binomial tree and least squares Monte Carlo approach. For purpose of assessing the performance of the model, two Euro-convertible bonds issued by Taiwan companies are chosen as samples and the difference between the theoretical price and market price during its issue period are provided. The results demonstrate that in spite of pretty slight overestimation, the least squares Monte Carlo simulation does a better job. In addition, this paper performs several kinds of sensitivity analysis to have in-depth understanding about the models. The consequence shows that the volatility of a stock return and the correlation between stock and exchange rate play a central role in ECB valuations.

Ce mémoire porte sur la mise au point de plateforme microfluidique couplée à la microscopie Raman confocale, utilisée dans des conditions d’excitation de la diffusion Raman (diffusion Raman exaltée de surface), dans le but d’obtenir une détection de très haute sensibilité d’espèces moléculaires sous écoulement dans des canaux de dimensions micrométriques. Ce travail a pour ambition de démontrer la faisabilité d’un couplage microscopie Raman/microfluidique en vue de la caractérisation in-situ et locale, des espèces et des réactions mises en jeu dans les fluides en écoulement dans les microcanaux. Nous avons utilisé un microcanal de géométrie T, fabriqué par lithographie douce, dans lequel sont injectées, à vitesse constante, des nanoparticules métalliques d’or ou d’argent dans une des deux branches du canal et une solution de pyridine ou de péfloxacine dans l’autre branche. La laminarité et la stationnarité du processus nous ont permis de cartographier la zone de mélange et de mettre en évidence l’exaltation du signal de diffusion Raman de la pyridine et de la péfloxacine, obtenue grâce aux nanoparticules métalliques, dans cette zone d’interdiffusion. L’enregistrement successif de la bande d’absorption des nanoparticules d’argent (bande plasmon) et du signal de diffusion Raman de la péfloxacine, en écoulement dans un microcanal, nous a permis d’établir un lien entre la morphologie des nanostructures métalliques, et plus précisément l’état d’agrégation des nanoparticules d’argent, et l’exaltation du signal Raman de la péfloxacine observé. Nous avons alors modifié la géométrie du canal afin d’y introduire une solution d’électrolyte (NaCl et NaNO3) et de modifier localement la charge de surface des colloïdes d’argent en écoulement. Nous avons ainsi confirmé que la modification de l’état d’agrégation des nanoparticules d’argent, induite par l’ajout contrôlé de solutions d’électrolytes, permet d’amplifier le signal SERS de la péfloxacine et d’optimiser la détection en microfluidique. Enfin, nous avons développé une seconde approche qui consistait à mettre en place une structuration métallisée des parois d’un microcanal. Nous avons ainsi démontré que la fonctionnalisation chimique de surface via un organosilane (APTES) permettait de tapisser le canal avec des nanoparticules d’argent et d’amplifier le signal Raman des espèces en écoulement dans ce même microcanal. / This thesis focuses on the development of a microfluidic platform coupled with confocal Raman microscopy, used in excitation conditions of Raman scattering (Surface enhanced Raman scattering, SERS) in order to gain in the detection sensitivity of molecular species flowing in channels of micrometer dimensions. This work aims to demonstrate the feasibility of coupling Raman microscopy / microfluidics for the in situ and local characterization of species and reactions taking place in the fluid flowing in microchannels. We used a T-shaped microchannel, made by soft lithography, in which gold or silver nanoparticles injected at constant speed, in one of the two branches of the channel and a solution of pyridine or pefloxacin in the other one. The laminar flow and the stationarity of the process allowed us to map the mixing zone and highlight the enhancement of the Raman signal of pyridine and pefloxacin, due to the metallic nanoparticles, in the interdiffusion zone. The recording of the both absorption band of the silver nanoparticles (plasmon band) and the Raman signal of pefloxacin, flowing in microchannel, allowed us to establish a link between the shape of the metallic nanostructure, and more precisely the silver nanoparticle aggregation state, and the enhancement of the Raman signal of pefloxacin observed. We then changed the channel geometry to introduce an electrolyte solution (NaCl and NaNO3) and locally modify the surface charge of the colloids. We have put in evidence that the change of the silver nanoparticle aggregation state, induced by the controlled addition of electrolyte solutions, could amplify the SERS signal of pefloxacin and thus optimizing the detection in microfluidics. At last, we established second a approach that consists in the metallic structuring of microchannel walls. This has shown that the surface chemical functionalization through organosilanes (APTES) allowed the pasting of the channel with silver nanoparticles, thus amplifying the Raman signal of the species flowing within the same microchannel.

信用衍生性商品在市場上交易漸趨熱絡，創新速度更是一日千里，市場上琳琅滿目的信用衍生性商品，投資人要如何審慎客觀評估風險後再檢視自身能承擔的風險後投資，諸如此類的議題在近幾年備受關注。尤其在2007金融海嘯之後，所有信用衍生性產品也無一倖免，信用評等公司對信用衍生性產品的評價，也備受挑戰，因此，辨識風險以及驅避風險在後金融海嘯時期，已是一刻不容緩之待解決問題。固定比例債務債券(Constant Proportion Debt Obligations; CPDO)亦是金融海嘯前一年所發明的創新信用衍生性商品，由於其高收益特性以及強調極低投資風險，吸引了許多投資人爭相購買，但金融海嘯時期，也是付之一炬。為了使投資人更了解此商品的風險，本研究運用在跳躍擴散模型假設下，存在封閉解的雙出場障礙式選擇權複製此商品的風險因子，並且為了描述此商品具有動態調整槓桿的時間相依(Time Dependent)性質，加入了蒙地卡羅模擬法，捕捉任意時點上，投資人面臨的風險，將風險因子拆解選擇權後，也更能讓投資人能以投資選擇權的知識運用到此商品來操作。最後，為了使投資人趨避諸如金融海嘯時期的風險，本研究也用選擇權的Delta 避險策略，替商品虛擬一現貨市場，並模擬出其避險之績效。 / The increasing trading volumes and innovative structures of credit derivatives have attracted great academic attention in the quantification and analysis of their complex risk characteristics. The pricing and hedging issues of complex credit structuers after the 2009 financial crisis are especially vital, and they present great challegens to both the academic community and industry practitioners. Constant Proportion Debt Obligations (CPDOs) are one of the new credit-innovations that claim to provide risk-adverse investors with fixed-income cash flows and minimal risk-bearing, yet the cash-outs events of such products during the crisis unfolded risk characteristics that had been unseen to investors. This research focuses on the pricing risk quantification, and dynamic hedging issues of CPDOs under a Levy jump diffusion setting. Based on decomposing the product's risk structure, we derive explicit closed-form solutions in the form of time-dependent double digital knock-out barrier options. This enables us to explore, in terms of the associated hedging greeks, the embeded risk characteristics of CPDOs and propose feasible delta-netral strategies that are feasible to hedge such products. Numerical simulations are subsequently performed to provide benchmark measures for the proposed hedging strategies.

本文實證探討黃金期貨報酬率的特性並在標的黃金期貨價格遵循狀態轉換跳躍擴散過程時實現美式選擇權之評價。在這樣的動態過程下，跳躍事件被一個複合普瓦松過程與對數常態跳躍振幅所描述，以及狀態轉換到達強度是由一個其狀態代表經濟狀態的隱藏馬可夫鏈所捕捉。考量不同的跳躍風險假設，我們使用Merton測度與Esscher轉換推導出在一個不完全市場設定下的風險中立黃金期貨價格動態過程。為了達到所需的精確度，最小平方蒙地卡羅法被用來近似美式黃金期貨選擇權的價值。基於實際市場資料，我們提供實證與數值結果來說明這個動態模型的優點。 / This dissertation empirically investigates the characteristics of gold futures returns and achieves the valuation of American-style options when the underlying gold futures price follows a regime-switching jump-diffusion process. Under such dynamics, the jump events are described as a compound Poisson process with a log-normal jump amplitude, and the regime-switching arrival intensity is captured by a hidden Markov chain whose states represent the economic states. Considering the different jump risk assumptions, we use the Merton measure and Esscher transform to derive risk-neutral gold futures price dynamics under an incomplete market setting. To achieve a desired accuracy level, the least-squares Monte Carlo method is used to approximate the values of American gold futures options. Our empirical and numerical results based on actual market data are provided to illustrate the advantages of this dynamic model.

Schwarz (1997)提出均數回復過程（Mean-Reverting Process, MR）捕捉能源價格的動態過程，而Lucia and Schwarz (2002)將此模型結合確定季節性函數，並推導出期貨價格封閉解。然而，能源價格常會因為未預期事件的發生而產生大幅度的變動，為了描述價格跳躍的現象，Clewlow and Strickland (2000)延伸Schwarz的模型提出均數回復跳躍擴散模型（Mean-reverting jump diffusion process, MRJD），此模型除了保留均數回復模型對能源價格會回復至長期水準的描述外，再加上跳躍項來描述價格的異常變動。而Cartea and Figueroa (2005)則同時考慮季節性和跳躍因子，並推導出期貨價格封閉解。另外，雖然台灣目前並非京都議定書所規範的國家，但環境保護是未來的趨勢，故在衡量能源產業財務風險時，除了考慮相關原料和產品，應考慮碳權交易之影響。為了探討財務風險管理在能源產業之應用，本文以煉油廠為例，將其表示成特定期貨部位的投資組合，並透過計算投資組合風險值來衡量煉油廠的財務風險。文中使用結合季節性的均數回復過程、均數回復跳躍擴散過程進行模型配適。實證結果顯示，均數回復跳躍擴散模型在回溯測試下表現最佳；另外，考慮碳權交易後會使得煉油廠的財務風險上升。 / Schwarz (1997) proposes the mean-reverting process (MR) to model energy spot price dynamics, and Lucia and Schwarz (2002) extend this model by including mean reversion and a deterministic seasonality. This model can capture the mean-reversion of energy price, but fail to account for the huge and non-negligible price movement in the market. Clewlow and Strickland (2000) extend Schwarz’s model to mean-reverting jump diffusion process (MRJD). Cartea and Figueroa (2005) present a model which captures the most importance characteristics of energy spot prices such as mean reversion, jumps and seasonality, and provide a closed-form solution for the forward. Although Taiwan is not the member of Kyoto Protocol, but Environmental Protection is a trend in the future. In order to measure the financial risk induced by energy industries, we should consider the effect of emission trading. In this paper, we discuss the implication of financial risk management in energy industries by analyzing the exposure of refinery which represented certain energy futures portfolios. We use MR and MRJD process with seasonality to model energy spot price dynamics, and calibrate the parameters to historical data. And, we consider the interaction of all of positions and calculate the Value-at-Risk of portfolios. The results show that among various approaches the MRJD presents more efficient results in back-testing, and emission trading poses additional risk factors which will increase the financial risk for refineries.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.