Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

“Green preservatives” – combating fungi in the food industry by applying antifungal lactic acid bacteria

Fungal spoilage is the most common type of microbial spoilage in food leading to significant economical and health problems throughout the world. Fermentation by lactic acid bacteria (LAB) is one of the oldest and most economical methods of producing and preserving food. Thus, LAB can be seen as an interesting tool in the development of novel bio-preservatives for food industry. The overall objective of this study was to demonstrate, that LAB can be used as a natural way to improve the shelf-life and safety of a wide range of food products. In the first part of the thesis, 116 LAB isolates were screened for their antifungal activity against four Aspergillus and Penicillium spp. commonly found in food. Approximately 83% of them showed antifungal activity, but only 1% showed a broad range antifungal activity against all tested fungi. The second approach was to apply LAB antifungal strains in production of food products with extended shelf-life. L. reuteri R29 strain was identified as having strong antifungal activity in vitro, as well as in sourdough bread against Aspergillus niger, Fusarium culmorum and Penicillium expansum. The ability of the strain to produce bread of good quality was also determined using standard baking tests. Another strain, L. amylovorus DSM19280, was also identified as having strong antifungal activity in vitro and in vivo. The strain was used as an adjunct culture in a Cheddar cheese model system and demonstrated the inhibition of P. expansum. Significantly, its presence had no detectable negative impact on cheese quality as determined by analysis of moisture, salt, pH, and primary and secondary proteolysis. L. brevis PS1 a further strain identified during the screening as very antifungal, showed activity in vitro against common Fusarium spp. and was used in the production of a novel functional wortbased alcohol-free beverage. Challenge tests performed with F. culmorum confirmed the effectiveness of the antifungal strain in vivo. The shelf-life of the beverage was extended significantly when compared to not inoculated wort sample. A range of antifungal compounds were identified for the 4 LAB strains, namely L. reuteri ee1p, L. reuteri R29, L. brevis PS1 and L. amylovorous DSM20531. The identification of the compounds was based on liquid chromatography interfaced to the mass spectrometer and PDA detector

Computational modeling of defects in nanoscale device materials

This PhD thesis concerns the computational modeling of the electronic and atomic structure of point defects in technologically relevant materials. Identifying the atomistic origin of defects observed in the electrical characteristics of electronic devices has been a long-term goal of first-principles methods. First principles simulations are performed in this thesis, consisting of density functional theory (DFT) supplemented with many body perturbation theory (MBPT) methods, of native defects in bulk and slab models of In0.53Ga0.47As. The latter consist of (100) - oriented surfaces passivated with A12O3. Our results indicate that the experimentally extracted midgap interface state density (Dit) peaks are not the result of defects directly at the semiconductor/oxide interface, but originate from defects in a more bulk-like chemical environment. This conclusion is reached by considering the energy of charge transition levels for defects at the interface as a function of distance from the oxide. Our work provides insight into the types of defects responsible for the observed departure from ideal electrical behaviour in III-V metal-oxidesemiconductor (MOS) capacitors. In addition, the formation energetics and electron scattering properties of point defects in carbon nanotubes (CNTs) are studied using DFT in conjunction with Green’s function based techniques. The latter are applied to evaluate the low-temperature, low-bias Landauer conductance spectrum from which mesoscopic transport properties such as the elastic mean free path and localization length of technologically relevant CNT sizes can be estimated from computationally tractable CNT models. Our calculations show that at CNT diameters pertinent to interconnect applications, the 555777 divacancy defect results in increased scattering and hence higher electrical resistance for electron transport near the Fermi level.