This thesis includes three chapters on electricity and natural gas prices. In the first chapter, we give a brief introduction to the characteristics of power prices and propose a mean reversion jump diffusion model, in which jump intensity depends on temperature data and overall system load, to model electricity prices. Compared to the models used in the literature, we find the model proposed in this chapter is better to capture the tail behavior in the electricity prices. In the second chapter, we use the model proposed in the first chapter to simulate the spark spread option and value the power generations. In order to simulate power generation, we first propose and estimate mean reversion jump diffusion model for natural gas prices, in which jump intensity is defined as a function of temperature and storage. Combing the model with the electricity models in chapter 1, we find that the value of power generation is closer to the real value of the power plants as reflected in the recent market transaction than one obtains from many other models used in literature. The third chapter investigates extremal dependence among the energy market. We find a tail dependence that exceeds the Pearson correlation ρ, which means the traditional Pearson correlation is not appropriate to model tail behavior of oil, natural gas and electricity prices. However, asymptotic dependence is rejected in all pairs except Henry Hub gas return and Houston Ship Channel gas return. We also find that extreme value dependence in energy market is stronger in bull market than that in bear market due to the special characteristics in energy market, which conflicts the accepted wisdom in equity market that tail correlation is much higher in periods of volatile markets from previous literature.

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The focus of this research was to investigate the effect of thermal degradation upon the mechanical properties of natural rubber compounds and apply those effects to the life prediction of off axis 2-ply cord rubber laminates. The work examined both the quasi-static and dynamic mechanical properties of two natural rubber vulcanizates, which had been subjected to isothermal anaerobic aging. Thermal aging was performed on two different natural rubber vulcanizates. The thermal aging was conducted between the temperatures of 80 and 120°C for times ranging from 3 to 24 days. The effect of thermal degradation was measured from the changes in the chemical composition of the vulcanizates as functions of time at temperature. A master curve relationship between the changes in the chemical composition of the vulcanizates due to thermal degradation and their static and dynamic mechanical properties has been developed. This relationship allowed for the prediction of the vulcanizate mechanical properties after thermal aging. It was found that the mechanical properties correlated with the percentage of poly and monosulfidic crosslinks, where in general higher levels of polysulfidic crosslink gave rise to the highest mechanical properties. Crack propagation in an aged and unaged natural rubber vulcanizate was measured using a double cantilever beam, DCB. This type of testing arrangement exhibits a plane strain condition and resulted in crack growth rates two orders of magnitude faster than traditional plane stress testing geometries. To validate the DCB specimens, an investigation into the potential cavitation inside the rubber of the DCB specimens was performed. It was found that no cavitation occurred due to the high speed of the fracture. DCB samples were thermally aged to determine the effect of thermal aging upon the crack growth rate. It was found that crack growth rates increase with thermal aging. Life prediction of the aged 2-ply laminates was performed using a finite element analysis. In order to verify the finite element models used in the life prediction, the fatigue failure and crack growth characteristics of off axis 2-ply cord-rubber laminates were examined with a delamination analysis. This analysis allowed for the determination of the modulus of off axis 2-ply laminates in the presence of damage as well as the calculation of the crack growth rates of the laminate. The failure of unaged and thermally aged 2-ply laminates was evaluated and compared to the crack growth rates of thermally aged DCB specimens. The trend due to thermal aging between the two types of testing specimens was consistent. The finite element analysis was sectioned into two approaches: crack initiation and crack propagation. The former utilized a residual strength approach, while the latter applied a fracture mechanics approach. The predicted stress versus cycles, S-N, curves were not in complete agreement with the experimental data. The error between the predicted and the experimental is discussed and future work to correct that error is suggested. While there was not complete agreement between the predicted and the experimental data, this dissertation outlines a comprehensive approach to track the effects of thermal degradation and apply those effects to a real world application. / Ph. D.

Os aços maraging são aços de baixo teor de carbono com estrutura martensítica (CCC), que são endurecidos pela precipitação de fases intermetálicas. O objetivo deste trabalho é estudar as transformações de fases desses aços: precipitação, reversão da martensita para a austenita e transformação martensítica. Nesse trabalho, foram caracterizadas uma corrida de aço maraging da série 300 e três corridas da série 350, usando diversas técnicas complementares: microscopia ótica, microscopia eletrônica de varredura com análise dispersiva de energia, microdurômetro, difração de raios-X, ferritoscópio e dilatometria. Os resultados obtidos mostraram que as corridas com maiores teores de cobalto e titânio apresentaram maiores valores de microdureza nos estados solubilizado e envelhecido. Por outro lado, medidas dilatométricas mostraram que há uma influência significativa tanto da composição química, quanto da taxa de aquecimento nas reações de precipitação e reversão da martensita para a austenita. No entanto, a transformação martensítica mostrou-se dependente apenas da taxa de aquecimento. / Maraging steels are steels with a low carbon martensitic structure (BCC), which are hardened by precipitation of intermetallic phases. The aim of this work is to study the phase transformations of these steels: precipitation, martensite to austenite reversion and martensitic transformation. In this study, one cast of 300 grade and three casts of 350 grade were characterized using several complementary techniques: optical microscopy, scanning el ectron microscopy with energy dispersive analysis, microhardness, X-ray diffraction, ferritoscope and dilatometry. The results showed that the casts with higher concentrations of cobalt and titanium showed higher microhardness in the solution annealed and aged states. On the other hand, dilatometry measurements showed that there is a significant influence of both the chemical composition and the heating rate on the reactions of precipitation and reversion of martensite to austenite. However, the martensitic transformation was dependent solely on the heating rate.

Os aços maraging são aços de baixo teor de carbono com estrutura martensítica (CCC), que são endurecidos pela precipitação de fases intermetálicas. O objetivo deste trabalho é estudar as transformações de fases desses aços: precipitação, reversão da martensita para a austenita e transformação martensítica. Nesse trabalho, foram caracterizadas uma corrida de aço maraging da série 300 e três corridas da série 350, usando diversas técnicas complementares: microscopia ótica, microscopia eletrônica de varredura com análise dispersiva de energia, microdurômetro, difração de raios-X, ferritoscópio e dilatometria. Os resultados obtidos mostraram que as corridas com maiores teores de cobalto e titânio apresentaram maiores valores de microdureza nos estados solubilizado e envelhecido. Por outro lado, medidas dilatométricas mostraram que há uma influência significativa tanto da composição química, quanto da taxa de aquecimento nas reações de precipitação e reversão da martensita para a austenita. No entanto, a transformação martensítica mostrou-se dependente apenas da taxa de aquecimento. / Maraging steels are steels with a low carbon martensitic structure (BCC), which are hardened by precipitation of intermetallic phases. The aim of this work is to study the phase transformations of these steels: precipitation, martensite to austenite reversion and martensitic transformation. In this study, one cast of 300 grade and three casts of 350 grade were characterized using several complementary techniques: optical microscopy, scanning el ectron microscopy with energy dispersive analysis, microhardness, X-ray diffraction, ferritoscope and dilatometry. The results showed that the casts with higher concentrations of cobalt and titanium showed higher microhardness in the solution annealed and aged states. On the other hand, dilatometry measurements showed that there is a significant influence of both the chemical composition and the heating rate on the reactions of precipitation and reversion of martensite to austenite. However, the martensitic transformation was dependent solely on the heating rate.

<p dir="ltr">Statistical arbitrage is a prevalent trading strategy which takes advantage of mean reverse property of spreads constructed from pairs or portfolios of assets. Utilizing statistical models and algorithms, statistical arbitrage exploits and capitalizes on the pricing inefficiencies between securities or within asset portfolios. </p><p dir="ltr">In chapter 2, We propose a framework for constructing diversified portfolios with multiple pairs trading strategies. In our approach, several pairs of co-moving assets are traded simultaneously, and capital is dynamically allocated among different pairs based on the statistical characteristics of the historical spreads. This allows us to further consider various portfolio designs and rebalancing strategies. Working with empirical data, our experiments suggest the significant benefits of diversification within our proposed framework.</p><p dir="ltr">In chapter 3, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and subsequently liquidating positions, all while considering the impact of transaction costs. Then we leverages a refined signature optimal stopping method to resolve this sequential optimal stopping problem, thereby unveiling the precise entry and exit timings that maximize gains. Our framework operates without any predefined assumptions regarding the dynamics of the underlying mean-reverting spreads, offering adaptability to diverse scenarios. Numerical results are provided to demonstrate its superior performance when comparing with conventional mean reversion trading rules.</p><p dir="ltr">In chapter 4, we introduce an innovative model-free and reinforcement learning based framework for statistical arbitrage. For the construction of mean reversion spreads, we establish an empirical reversion time metric and optimize asset coefficients by minimizing this empirical mean reversion time. In the trading phase, we employ a reinforcement learning framework to identify the optimal mean reversion strategy. Diverging from traditional mean reversion strategies that primarily focus on price deviations from a long-term mean, our methodology creatively constructs the state space to encapsulate the recent trends in price movements. Additionally, the reward function is carefully tailored to reflect the unique characteristics of mean reversion trading.</p>

La pression toxique induite par les perturbateurs endocriniens sur l’environnement ainsi que sur la santé de l’homme a augmenté de manière significative durant les dernières décennies. Il est devenu urgent de mettre en place des outils pour détecter et surveiller les perturbateurs endocriniens et pour déterminer la possibilité de cause de perturbations endocriniennes pour les produits chimiques nouvellement introduits. Le développement de nouveaux tests biologiques in vivo en utilisant les larves d'organismes aquatiques tels que medaka (Oryzias latipes) ou Xenopus laevis semble être une stratégie adéquate pour identifier les perturbateurs endocriniens. Durant cette thèse, trois nouveaux modèles transgéniques à base de l’embryon de medaka ont été développés. Le modèle transgénique de medaka ChgH -gfp permet la détection rapide des œstrogènes et des inhibiteurs de l'aromatase en seulement 24 heures avec une sensibilité de 15 ng / L d’éthinylestradiol. Le modèle transgénique de medaka 42sp50-gfp_CgH-gfp montre une fluorescence dans le foie en réponse aux œstrogènes, en plus de la fluorescence émise dans les œufs en développement. C’est donc un système approprié pour étudier le lien entre la signalisation de l'axe ostrogénique et des aberrations de la détermination du sexe chez les poissons. Un embryon transgénique de medaka spiggin - GFP a aussi été développé pour détecter les androgènes et anti-androgènes dans un test de 96 heures avec une sensibilité de 1,5 ug / L de 17α–méthyl testostérone et 276 ug / L de flutamide. Les nouveaux modèles de medaka transgéniques rapporteurs développés dans cette thèse permettent une détection rapide, simple et fiable des perturbateurs d'axe ostrogénique, androgénique et de l’aberration de détermination du sexe chez le medaka. Ils ont été appliqués pour détecter les perturbateurs endocriniens dans les eaux de surface de l'environnement et pour évaluer le rôle potentiel des produits chimiques dans les perturbations endocriniennes. Cela a permis de démontrer l’applicabilité de ces embryons fluorescents comme outils biologiques dans la procédure de détection et la caractérisation des perturbateurs endocriniens. / The toxic pressure of endocrine disruptors on biodiversity and human health has increased significantly over recent decades. As a consequence tools are needed to detect and monitor endocrine disruptors in surface water and to determine the endocrine disrupting potential of newly introduced chemicals. Fish and amphibian larvae, notably the medaka (Oryzias latipes) and Xenopus laevis, offer multiple advantages in this context. In the research carried out in the context of this thesis, different novel medaka-based transgenic models were developed. First, transgenic ChgH-gfp medaka model was designed and optimized for the rapid detection of estrogens and aromatase inhibitors. The model shows significant response within 24 hours with a sensitivity of 15 ng/L ethinylestradiol. Second, a double transgenic 42sp50-gfp_ChgH-gfp medaka which exhibits fluorescence both in the liver in response to estrogens and in developing oocytes as a function of phenotypic sex. It is therefore a suitable model for studying the link between estrogen axis signalling and aberrations of sex determination in fish. Third, a novel spiggin-gfp medaka model was developed to detect androgens and anti-androgens. This model can be exploited in a 96-hour assay with a sensitivity of 1.5 μg/L 17α- methyltestosterone and 276 μg/L flutamide. The novel transgenic medaka models developed in this thesis allow rapid, simple and reliable detection of estrogen and androgen axis disruption and aberrations in medaka sex determination. They have been successfully applied to detect endocrine disruptors in environmental surface water and to assess chemicals with unknown endocrine disrupting potential. Taken together these results demonstrate the applicability of medaka reporter larvae as biological tools in the procedure of detection and characterization of endocrine disruptors.

Most of the notations and terminological conventions used in this thesis are Statistical. The aim in risk management is to describe the risk factors present in time series. In order to group these risk factors, one needs to distinguish between different stochastic processes and put them into different classes. The risk factors discussed in this thesis are fat tails and mean reversion. The presence of these risk factors fist need to be found in the historical dataset. I will refer to the historical dataset as the original dataset. The Ljung- Box-Pierce test will be used in this thesis to determine if the distribution of the original dataset has mean reversion or no mean reversion. / Mathematical Sciences / M.Sc. (Applied Mathematics)

This thesis studies different aspects of firm decisions by using a dynamic model. I estimate a dynamic model of the firm based on the trade-off theory of capital structure that endogenizes investment, leverage, and payout decisions. For the estimation of the model I use Efficient Method of Moments (EMM), which allows me to recover the structural parameters that best replicate the characteristics of the data. I start analyzing the question of whether target leverage varies over time. While this is a central issue in finance, there is no consensus in the literature on this point. I propose an explanation that reconciles some of the seemingly contradictory empirical evidence. The dynamic model generates a target leverage that changes over time and consistently reproduces the results of Lemmon, Roberts, and Zender (2008). These findings suggest that the time-varying target leverage assumption of the big bulk of the previous literature is not incompatible with the evidence presented by Lemmon, Roberts, and Zender (2008). Then I study how corporate income tax payments vary with the corporate income tax rate. The dynamic model produces a bell-shaped relationship between tax revenue and the tax rate that is consistent with the notion of the Laffer curve. The dynamic model generates the maximum tax revenue for a tax rate between 36% and 41%. Finally, I investigate the impact of financial constraints on investment decisions by firms. Model results show that investment-cash flow sensitivity is higher for less financially constrained firms. This result is consistent with Kaplan and Zingales (1997). The dynamic model also rationalizes why large and mature firms have a positive and significant investment-cash flow sensitivity.

本研究的目的，在於檢視購併案產生後，企業的報酬是否會受到平均數復歸（Mean reversion）的影響，而逐漸回復到產業的平均報酬。並且分析主併公司與被併公司佔雙方總資產比例的高低差異，所受到的不同影響程度。 本次研究的樣本採用1987～2006年中的美國電子電機產業共77件購併案，並依照主併公司佔雙方總資產的比例不同，分成為兩個群集。將兩群集做比較分析。實證結果顯示，兩個群集均有顯著的平均數復歸現象。而主併佔雙方總資產比例較高的群集，在購併第一年即有顯著的優於產業平均報酬，而主併與被併資產相近的群集，則是於第四年開始才有顯著的績效改善。根據實證結果，我們做出以下的結論： 1.企業的報酬具有平均數復歸的特性，表現優良的公司會被他人學習，而使整體產業平均報酬逐漸提升，漸漸蠶食原先與產業平均之間的差距；相反的，表現不佳的公司亦透過學習，逐漸改善自己的績效，也使的整體產業平均報酬上升，最後雙方都將趨向產業的平均水準。 2.當研究者要分析企業遭受偶發性事件（如購併）的影響時，應當考慮平均數復歸的所帶來的效果。如果忽略了平均數復歸所帶來的效果，將會對事件產生的影響給予錯誤的解讀。 3.面對購併績效的研究時，必須移除平均數復歸的負面效果，如此才得以正確估計購併後的績效表現。且此時主併公司資產佔雙方資產比例較高者，於購併第一年就有明顯的績效改善的效果，而雙方資產相近者，則在購併成立後第四年開始才有較佳的績效表現。 / The purpose of this research is to look over the return of enterprise can receive influence from mean reversion on post-merger performance. And it analyzes the degree of influence on acquirer companies with different proportion in total assets of both acquirer and target companies. The sample of this research adopts 77 cases of electronic and electrical equipment industry of U.S.A. in 1987- 200, take according to the proportion of total assets of acquirer company in both total assets of acquirer and target company, divide into two clusters. Make comparative analysis of these two clusters. According to the empirical results, we make the following conclusions: 1.The return of enterprises has characteristic of mean reversion. Both well performed companies and worse performed companies will move toward the whole industry's average return. 2.As the researcher wants to analyze the influence of enterprises suffered from the sporadic incident (such as M&A), they should consider the phenomenon of mean reversion. Take off the negative result of the mean reversion in order to estimate correctly for the exactly performance after M&A. 3.The acquirer companies which total assets have a higher proportion in both acquirer and target companies, will have superior to industry average return apparently in first year, and the acquirer companies which total assets close to the target companies, will have apparent improvement in performances until the fourth year.