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Realistisches Rendering stellt einen wichtigen Unterzweig der Computergrafik dar. Durch globale Beleuchtung sind heutzutage gute Ergebnisse erzielbar, allerdings muss dafür in der Regel eine lange Berechnungszeit in Kauf genommen werden. Verfahren wie Instant Radiosity nutzen die Leistungsfähigkeit heutiger Grafikhardware, um die Berechnungszeiten zu verkürzen. Durch Verwendung virtueller Punktlichtquellen kann eine Approximation der globalen Beleuchtung erzielt werden. Allerdings wird hierbei von einer expliziten Berechnung der Sichtbarkeit ausgegangen, die sich schnell zum Flaschenhals des Verfahrens entwickelt. Antiradiance-Splatting -- das in dieser Arbeit vorgestellte Verfahren -- arbeitet ebenfalls mit virtuellen Lichtquellen; dabei wird aber versucht, die Kosten für die explizite Berechnung der Sichtbarkeit einzusparen. Zu die...
Für diese Studienarbeit wurde ein Renderer entwickelt, der Deferred Shading, Interleaved Sampling und Anti-Aliasing unterstützt. Durch unabhängige Implementierung können die einzelnen Verfahren in andere Programme integriert werden, was anhand einer Beispielanwendung illustriert wird. Deferred Shading ist ein Verfahren, dass die Effizienz von Rendering-Prozessen mit hohen Shading-Kosten erhöht. Auf moderner Grafik-Hardware ist eine direkte Implementierung möglich. Interleaved Sampling ist ein allgemeines Verfahren, um aufwändige Abtastschemata effizient auf Grafik-Hardware zu implementieren. Während der Fokus bei Deferred Shading vor allem auf Rendering-Effizienz liegt, zielt Interleaved Sampling auch auf eine gesteigerte Rendering-Qualität ab. Anti-Aliasing-Verfahren wie Multi-Sampling dienen vornehmlich dem Zweck, die Bildqualität zu...
Minimal martingale measure Shot-noise process Jump diffusion
This paper considers the pricing and hedging of collateralized debt obligations (CDOs). CDOs are complex derivatives on a pool of credits which we choose to analyse in the top down model proposed in Filipovic et al. (Math. Finance, forthcoming, 2009). We reflect on the implied forward rates and bring them in connection with the top-down framework in Lipton and Shelton (Working paper, 2009) and Schonbucher (Working paper, ETH Zurich, 2005). Moreover, we derive variance-minimizing hedging strategies for hedging single tranches with the full index. The hedging strategies are given for the general case. We compute them also explicitly for a parsimonious one-factor affine model.
In order to arrange matter with nanometer precision, self organization is the most powerful strategy. For this, DNA is an outstanding material as it is a cheap, programmable, biocompatible and well understood polymer and therefore became the basis for a fast growing field: DNA-nanotechnology. The aim of this thesis was to develop new types of interactions for DNA nanotechnology and to build up structures from DNA minicircles, a so far neglected construction element. ...
We propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds. Further on, we study a model for portfolio credit risk where we consider both firm specific and systematic risks. The model generalizes the attempt from Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering of defaults. Then, we show how to price first-to-def...
This work proposes term structure models consisting of two parts: a part which can be represented in exponential quadratic form and a shot noise part. These term structure models allow for explicit expressions of various derivatives. In particular, they are very well suited for credit risk models. The goal of the paper is twofold. First, a number of key building blocks useful in term structure modelling are derived in closed-form. Second, these building blocks are applied to single and portfolio credit risk. This approach generalizes Duffie & Garleanu (2001) and is able to produce realistic default correlation and default clustering. We conclude with a specific model where all key building blocks are computed explicitly.
This work proposes term structure models consisting of two parts: a part which can be represented in exponential quadratic form and a shot noise part. These term structure models allow for explicit expressions of various derivatives. In particular, they are very well suited for credit risk models. The goal of the paper is twofold. First, a number of key building blocks useful in term structure modelling are derived in closed-form. Second, these building blocks are applied to single and portfolio credit risk. This approach generalizes Duffie & Garleanu (2001) and is able to produce realistic default correlation and default clustering. We conclude with a specific model where all key building blocks are computed explicitly.
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