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Es sei ein Heath-Jarrow-Morton Zinsstrukturmodell df(t,T) = alpha(t,T)dt + sigma(t,T)dX_t gegeben, angetrieben von einem mehrdimensionalen Semimartingal X. Das Ziel dieser Arbeit besteht darin, die Existenz endlich dimensionaler Realisierungen für solche Modelle zu untersuchen, wobei wir als treibende Prozesse die Klasse der Grigelionis Prozesse wählen, die insbesondere Levy Prozesse enthält. Zur Bearbeitung der Fragestellung werden zwei veschiedene Ansätze verfolgt. Wir dehnen die Ideen aus der Differenzialgeometrie von Björk und Svensson (2001) auf die vorliegende Situation aus und zeigen, dass das in der zitierten Arbeit bewiesene Kriterium für die Existenz endlich dimensionaler Realisierungen in unserem Fall als notwendiges Kriterium dienlich ist. Dieses Resultat wird auf konkrete Volatilitätsstrukturen angewandt. Im Kontext von sogenannten Benchmark Realisierungen, die eine natürliche Verallgemeinerung von Short Rate Realisierungen darstellen, leiten wir Integro-Differenzialgleichungen her, die für die Untersuchung der Existenz endlich dimensionaler Realisierungen hilfreich sind. Als Verallgemeinerung eines Resultats von Jeffrey (1995) beweisen wir außerdem, dass Zinsstrukturmodelle, die eine generische Benchmark Realisierung besitzen, notwendigerweise eine singuläre Hessesche Matrix haben. Beide Ansätze zeigen, dass neue Phänomene auftreten, sobald der treibende Prozess X Sprünge macht. Es gibt dann auf einmal nur noch sehr wenige Zinsstrukturmodelle, die endlich dimensionale Realisierungen zulassen, was ein beträchtlicher Unterschied zu solchen Modellen ist, die von einer Brownschen Bewegung angetrieben werden. Aus diesem Grund zeigen wir, dass für die in der Literatur oft behandelten Modelle mit deterministischer Richtungsvolatilität eine Folge von endlich dimensionalen Systemen existiert, die gegen das Zinsmodell konvergieren. / Let f(t,T) be a term structure model of Heath-Jarrow-Morton type df(t,T) = alpha(t,T)dt + sigma(t,T)dX_t, driven by a multidimensional semimartingale X. Our objective is to study the existence of finite dimensional realizations for equations of this kind. Choosing the class of Grigelionis processes (including in particular Levy processes) as driving processes, we approach this problem from two different directions. Extending the ideas from differential geometry in Björk and Svensson (2001), we show that the criterion for the existence of finite dimensional realizations, proven in the aforementioned paper, still serves as a necessary condition in our setup. This result is applied to concrete volatility structures. In the context of benchmark realizations, which are a natural generalization of short rate realizations, we derive integro-differential equations, suitable for the analysis of the realization problem. Generalizing Jeffrey (1995), we also prove a result stating that forward rate models, which generically possess a benchmark realization, must have a singular Hessian matrix. Both approaches reveal that, with regard to the results known for driving Wiener processes, new phenomena emerge, as soon as the driving process X has jumps. In particular, the occurrence of jumps severely limits the range of models that admit finite dimensional realizations. For this reason we prove, for the often considered case of deterministic direction volatility structures, the existence of finite dimensional systems converging to the forward rate model.

Terrestrial laser scanning (TLS) has been successfully used for three-dimensional (3D) data capture in forests for almost two decades. Beyond the plot-based data capturing capabilities of TLS, vehicle-based mobile laser scanning (MLS) systems have the clear advantage of fast and precise corridor-like 3D data capture, thus providing a much larger coverage within shorter acquisition time. This paper compares and discusses advantages and disadvantages of multi-temporal MLS data acquisition compared to established TLS data recording schemes. In this pilot study on integrated TLS and MLS data processing in a forest, it could be shown that existing TLS data evaluation routines can be used for MLS data processing. Methods of automatic laser scanner data processing for forest inventory parameter determination and quantitative structure model (QSM) generation were tested in two sample plots using data from both scanning methods and from different seasons. TLS in a multi-scan configuration delivers very high-density 3D point clouds, which form a valuable basis for generating high-quality QSMs. The pilot study shows that MLS is able to provide high-quality data for an equivalent determination of relevant forest inventory parameters compared to TLS. Parameters such as tree position, diameter at breast height (DBH) or tree height can be determined from MLS data with an accuracy similar to the accuracy of the parameter derived from TLS data. Results for instance in DBH determination by cylinder fitting yielded a standard deviation of 1.1 cm for trees in TLS data and 3.7 cm in MLS data. However, the resolution of MLS scans was found insufficient for successful QSM generation. The registration of MLS data in forests furthermore requires additional effort in considering effects caused by poor GNSS signal.

Insurance contracts will be reported at fair values on insurers’ balance sheets from 2010. In this thesis, we will review the conceptual and theoretical backbone of the insurance fair valuation project while providing a summary of the key features of the fair valuation project. Then, we will conduct a case study aimed at finding, under the fair valuation regime, the best asset allocation strategy for a particular business unit that carries a hypothetical annuity portfolio using a single modelling framework for valuation, risk calculation and business appraisal.