退休金是退休人未來生活的依靠，確保在退休後能得到適足的退休給付，政府在退休金上實施保證收益制度，此制度為最低保證利率與投資報酬率連結。本文探討退休金給付標準為確定提撥制，當退休金的投資報酬率是根據其連結之股價指數的表現來計算時，股價指數報酬率的模型假設為馬可夫調控跳躍過程模型，考慮市場狀態與布朗運動項、跳躍項的跳躍頻率相關，即為Elliot et al. (2007) 的模型特例。使用1999年至2012年的道瓊工業指數與S&P 500指數的股價指數對數報酬率作為研究資料，採用EM演算法估計參數及SEM演算法估計參數共變異數矩陣。透過概似比檢定說明馬可夫調控跳躍過程模型比狀態轉換模型、跳躍風險下狀態轉換模型更適合描述股價指數報酬率變動情形，也驗證馬可夫調控跳躍過程模型具有描述報酬率不對稱、高狹峰及波動叢聚的特性。最後，假設最低保證利率為固定下，利用Esscher轉換法計算不同模型下型I保證之確定提撥制退休金的評價公式，從公式中可看出受雇人提領的退休金價值可分為政府補助與個人帳戶擁有之退休金兩部分。以執行敏感度分析探討估計參數對於馬可夫調控跳躍過程模型評價公式的影響，而型II保證之確定提撥制退休金的價值則以蒙地卡羅法模擬並探討其敏感度分析結果。 / Pension plan make people a guarantee life in their retirement. In order to ensure the appropriate amount of pension plan, government guarantees associated with pension plan which ties minimum rate of return guarantees and underlying asset rate of return. In this paper, we discussed the pension plan with defined contribution (DC). When the return of asset is based on the stock indices, the return model was set on the assumption that markov-modulated jump diffusion model (MMJDM) could the Brownian motion term and jump rate be both related to market states. This model is the specific case of Elliot et al. (2007) offering. The sample observations is Dow-Jones industrial average and S&P 500 index from 1999 to 2012 by logarithm return of the stock indices. We estimated the parameters by the Expectation-Maximization (EM) algorithm and calculated the covariance matrix of the estimates by supplemented EM (SEM) algorithm. Through the likelihood ratio test (LRT), the data fitted the MMJDM better than other models. The empirical evidence indicated that the MMJDM could describe the asset return for asymmetric, leptokurtic, volatility clustering particularly. Finally, we derived different model's valuation formula for DC pension plan with type-I guarantee by Esscher transformation under rate of return guarantees is constant. From the formula, the value of the pension plan could divide into two segment: government supplement and employees deposit made pension to their personal bank account. And then, we done sensitivity analysis through the MMJDM valuation formula. We used Monte Carlo simulations to evaluate the valuation of DC pension plan with type-II guarantee and discussed it from sensitivity analysis.

可轉換公司債是一種在持有期間內，投資人可以在規定的時間內將債券轉換為股票，或是到期時得到債券報酬的一種複合式證券。因此，可轉債除了具有債券性質之外，還包含另一部份可視為一美式選擇權的股票選擇權。 本篇論文將可轉換債券評價結合數值分析中的最小蒙地卡羅法(Least square monte carlo)，使得在評價可轉債時，能夠具有更多的彈性處理發行公司自行設計的贖回條款與其他各種不同的契約情況。 此外，本篇論文針對股價考慮跳躍的性質，使用Compound Poisson 過程模擬發生跳躍的次數，導入Merton的跳躍模型(Jump-diffusion Model)，在Merton的假設下，模擬未來股價的動態變化。 信用風險方面，本文採用Duffie提出的風險CIR模型評價。考慮存活函數(Survival Function)和違約強度(Hazard Rate Function)，使用CIR模型描述信用違約強度在可轉債持有期間的動態變化，最後模擬出違約的時點，結合LSMC下的可轉債評價評價法。 最後利率部份，雖然Brennan and Schwartz(1980)認為隨機利率對於可轉換債券的評價，並沒有明顯的效果，反而會降低評價時的效率，但是為了符合評價過程的合理性，本文使用CIR短期利率模型。

Le travail présenté dans ce mémoire avait pour objectif d’étudier le processus de la pénétration d'eau dans les composites en carbone/époxyde dans un premier temps, et dans un deuxième temps, d’étudier l’effet de la prise en eau par ces matériaux sur les performances mécaniques des composites et leur joints collés. L'intégration de ces phénomènes physiques dans la modélisation numérique est d'une grande importance dans la prédiction de la durabilité d’une structure en composite subissant un vieillissement hygrothermique. Par conséquent, ce travail consiste non seulement en des observations expérimentales, mais aussi en des simulations numériques. Des corrélations entre les résultats obtenus permettent d’une part de mieux comprendre ce qui se passe dans un système composite avec l’assemblage collé soumis à des charges mécaniques, de l’initiation d’endommagement jusqu’à la rupture finale ; d'autre part, de valider un modèle numérique robuste dans le but de la conception et de l’optimisation. Les originalités de ce travail se situent à différents niveaux en proposant : 1. un nouveau modèle de diffusion à deux-phases permettant de mieux décrire l’effet de l’épaisseur des stratifiés sur la pénétration de l’eau; 2. un nouveau modèle RPM « Residual Property Model » afin de prévoir la dégradation des propriétés mécaniques due à la prise en eau ; 3. une nouvelle loi de traction-séparation linéaire-exponentiel pour décrire la courbe-R observée dans les essais DCB en mode I pur sur les composites stratifiés afin de les intégrer plus facilement dans les modèles numériques / Le travail présenté dans ce mémoire avait pour objectif d’étudier le processus de la pénétration d'eau dans les composites en carbone/époxyde dans un premier temps, et dans un deuxième temps, d’étudier l’effet de la prise en eau par ces matériaux sur les performances mécaniques des composites et leur joints collés. L'intégration de ces phénomènes physiques dans la modélisation numérique est d'une grande importance dans la prédiction de la durabilité d’une structure en composite subissant un vieillissement hygrothermique. Par conséquent, ce travail consiste non seulement en des observations expérimentales, mais aussi en des simulations numériques. Des corrélations entre les résultats obtenus permettent d’une part de mieux comprendre ce qui se passe dans un système composite avec l’assemblage collé soumis à des charges mécaniques, de l’initiation d’endommagement jusqu’à la rupture finale ; d'autre part, de valider un modèle numérique robuste dans le but de la conception et de l’optimisation. Les originalités de ce travail se situent à différents niveaux en proposant : 1. un nouveau modèle de diffusion à deux-phases permettant de mieux décrire l’effet de l’épaisseur des stratifiés sur la pénétration de l’eau; 2. un nouveau modèle RPM « Residual Property Model » afin de prévoir la dégradation des propriétés mécaniques due à la prise en eau ; 3. une nouvelle loi de traction-séparation linéaire-exponentiel pour décrire la courbe-R observée dans les essais DCB en mode I pur sur les composites stratifiés afin de les intégrer plus facilement dans les modèles numériques

Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs). Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM). Further, we demonstrate the usefulness of the extended Bayesian model (eBM) for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments.

Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs). Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM). Further, we demonstrate the usefulness of the extended Bayesian model (eBM) for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments.

<p>The miniaturization and thinning of wearable, soft robotics and medical devices are soon to require higher performance modeling as the physical flexibility causes direct impacts on the electrical characteristics of the circuit – changing its behavior. As a representative flexible electronic component, the organic field effect transistor (OFET) has attracted much attention in its manufacturing as well as applications. However, as the strain and stress effects are integrated into multiphysics modelers with deeper interactions, the computational complexity and accuracy of OFET modeling is resurfacing as a limiting bottleneck.</p><p>The dissertation was organized into three interrelated studies. In the first study, the Mass-Spring-Damper (MSD) model for an inverted staggered thin film transistor (TFT) was proposed to investigate the TFT’s internal stress/strain fields, and the strain effects on the overall characteristics of the TFT. A comparison study with the finite element analysis (FEA) model shows that the MSD model can reduce memory usage and raises the computational convergence speed for rendering the same results as the FEA. The second study developed the generalized solid-state model by incorporating the density of trap states in the band structure of organic semiconductors (OSCs). The introduction of trap states allows the generalized solid-state model to describe the electrical characteristics of both inorganic TFTs and organic field-effect transistors (OFETs). It is revealed through experimental verification that the generalized solid-state model can accurately characterize the bending induced electrical properties of an OFET in the linear and saturation regimes. The third study aims to model the transient and steady-state dynamics of an arbitrary organic semiconductor device under mechanical strain. In this study, the fractional drift-diffusion (Fr-DD) model and its computational scheme with high accuracy and high convergence rate were proposed. Based on simulation and experimental validation, the transconductance and output characteristics of a bendable OFET were found to be well determined by the Fr-DD model not only in the linear and saturation regimes, but also in the subthreshold regime.</p>

In this paper, Monte Carlo simulation for CCR (Counterparty Credit Risk) modeling is investigated. A jump-diffusion model, Bates' model, is used to describe the price process of an asset, and the counterparty default probability is described by a stochastic intensity model with constant intensity. In combination with Monte Carlo simulation, the variance reduction technique importance sampling is used in an attempt to make the simulations more efficient. Importance sampling is used for simulation of both the asset price and, for CVA (Credit Valuation Adjustment) estimation, the default time. CVA is simulated for both European and Bermudan options. It is shown that a significant variance reduction can be achieved by utilizing importance sampling for asset price simulations. It is also shown that a significant variance reduction for CVA simulation can be achieved for counterparties with small default probabilities by employing importance sampling for the default times. This holds for both European and Bermudan options. Furthermore, the regression based method least squares Monte Carlo is used to estimate the price of a Bermudan option, resulting in CVA estimates that lie within an interval of feasible values. Finally, some topics of further research are suggested. / I denna rapport undersöks Monte Carlo-simuleringar för motpartskreditrisk. En jump-diffusion-modell, Bates modell, används för att beskriva prisprocessen hos en tillgång, och sannolikheten att motparten drabbas av insolvens beskrivs av en stokastisk intensitetsmodell med konstant intensitet. Tillsammans med Monte Carlo-simuleringar används variansreduktionstekinken importance sampling i ett försök att effektivisera simuleringarna. Importance sampling används för simulering av både tillgångens pris och, för estimering av CVA (Credit Valuation Adjustment), tidpunkten för insolvens. CVA simuleras för både europeiska optioner och Bermuda-optioner. Det visas att en signifikant variansreduktion kan uppnås genom att använda importance sampling för simuleringen av tillgångens pris. Det visas även att en signifikant variansreduktion för CVA-simulering kan uppnås för motparter med små sannolikheter att drabbas av insolvens genom att använda importance sampling för simulering av tidpunkter för insolvens. Detta gäller både europeiska optioner och Bermuda-optioner. Vidare, används regressionsmetoden least squares Monte Carlo för att estimera priset av en Bermuda-option, vilket resulterar i CVA-estimat som ligger inom ett intervall av rimliga värden. Slutligen föreslås några ämnen för ytterligare forskning.

The text-guided diffusion model GLIDE (Guided Language to Image Diffusion for Generation and Editing) is the state of the art in text-to-image generative artificial intelligence (AI). GLIDE has rich representations, but medical applications of this model have not been systematically explored. If GLIDE had useful medical knowledge, it could be used for medical image analysis tasks, a domain in which AI systems are still highly engineered towards a single use-case. Here we show that the publicly available GLIDE model has reasonably strong representations of key topics in cancer research and oncology, in particular the general style of histopathology images and multiple facets of diseases, pathological processes and laboratory assays. However, GLIDE seems to lack useful representations of the style and content of radiology data. Our findings demonstrate that domain-agnostic generative AI models can learn relevant medical concepts without explicit training. Thus, GLIDE and similar models might be useful for medical image processing tasks in the future - particularly with additional domain-specific fine-tuning.