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.

Do selective cyclo-oxygenase-2 inhibitors and traditional non-steroidal anti-inflammatory drugs increase the risk of atherothrombosis? Meta-analysis of randomised trials

Objective: To assess the effects of selective cyclo-oxygenase-2 (COX 2) inhibitors and traditional non-steroidal anti-inflammatory drugs (NSAIDs) on the risk of vascular events. Design: Meta-analysis of published and unpublished tabular data from randomised trials, with indirect estimation of the effects of traditional NSAIDs. Data sources: Medline and Embase (January 1966 to April 2005); Food and Drug Administration records; and data on file from Novartis, Pfizer, and Merck. Review methods: Eligible studies were randomised trials that included a comparison of a selective COX 2 inhibitor versus placebo or a selective COX 2 inhibitor versus a traditional NSAID, of at least four weeks' duration, with information on serious vascular events (defined as myocardial infarction, stroke, or vascular death). Individual investigators and manufacturers provided information on the number of patients randomised, numbers of vascular events, and the person time of follow-up for each randomised group. Results: In placebo comparisons, allocation to a selective COX 2 inhibitor was associated with a 42% relative increase in the incidence of serious vascular events (1.2%/year v 0.9%/year; rate ratio 1.42, 95% confidence interval 1.13 to 1.78; P = 0.003), with no significant heterogeneity among the different selective COX 2 inhibitors. This was chiefly attributable to an increased risk of myocardial infarction (0.6%/year v 0.3%/year; 1.86, 1.33 to 2.59; P = 0.0003), with little apparent difference in other vascular outcomes. Among trials of at least one year's duration (mean 2.7 years), the rate ratio for vascular events was 1.45 (1.12 to 1.89; P = 0.005). Overall, the incidence of serious vascular events was similar between a selective COX 2 inhibitor and any traditional NSAID (1.0%/year v 0.9/%year; 1.16, 0.97 to 1.38; P = 0.1). However, statistical heterogeneity (P = 0.001) was found between trials of a selective COX 2 inhibitor versus naproxen (1.57, 1.21 to 2.03) and of a selective COX 2 inhibitor versus non-naproxen NSAIDs (0.88, 0.69 to 1.12). The summary rate ratio for vascular events, compared with placebo, was 0.92 (0.67 to 1.26) for naproxen, 1.51 (0.96 to 2.37) for ibuprofen, and 1.63 (1.12 to 2.37) for diclofenac. Conclusions: Selective COX 2 inhibitors are associated with a moderate increase in the risk of vascular events, as are high dose regimens of ibuprofen and diclofenac, but high dose naproxen is not associated with such an excess.

Bioengineering strategies to improve functional qualities of nisin

The abuse of antibiotics and the emergence of multi-drug resistant bacterial strains have created the need to explore alternative methods of controlling microbial pathogens. The bacteriocin family of antimicrobial peptides has been proposed as one such alternative to classic antibiotics. Nisin A belongs to the subgroup of bacteriocins called the lantibiotics, which contain several unusual amino acids as a consequence of enzyme-mediated post-translational modifications. As nisin is produced by generally regarded as safe (GRAS) microorganisms, it could potentially be applied in a clinical setting. However, as lantibiotics are naturally produced in such small quantities, this can hinder their industrial potential. In order to overcome this, several approaches can be utilised. For example, given the gene encoded nature of lantibiotics, genetic engineering approaches can be implemented in order to yield variants with enhanced properties. Here, the use of mutagenesis-based strategies was employed to obtain a derivative of nisin with enhanced bioactivity in vitro. Investigations with purified peptide highlighted the enhanced specific activity of this variant, nisin M21V, against food-borne Listeria monocytogenes strains. Furthermore, this specific enhanced bioactivity was evident in a mouse model of listeriosis. Reductions in bioluminescence and microbial counts in organs from infected mice were observed following treatment with nisin M21V compared to that of wild-type nisin A. Peptide bioengineering approaches were also implemented to obtain additional novel derivatives of nisin. The generation of “S5X” and “S33X” banks (representing a change of natural serines at positions 5 and 33 to all possible alternative residues) by a combination of site-saturation and site-directed mutagenesis led to the identification of several derivatives exhibiting improved stability. This allowed the rational design of variants with enhanced stability compared to that of wild type nisin. Another means of tackling issues associated with lantibiotic yield is to combine lantibiotics with other antimicrobials. This could circumvent the need for enhanced production while also reducing concentrations of the peptide antimicrobials. We observed that combinations of nisin variants and low levels of plant essential oils (thymol, carvacrol, trans-cinnamaldehyde) significantly controlled Gram negative foodborne pathogens in in vitro assays compared to nisin A-essential oil combinations. This enhanced control was also evident in model food systems. Nisin variants used in conjunction with carvacrol significantly reduced numbers of E. coli O157:H7 in apple juice while a commercial nisin preparation used in combination with citric acid significantly controlled C. sakazakii in infant milk formula. It is noteworthy that while nisin is generally associated with Gram positive targets, upon combination with plant essential oils the spectrum of inhibition was broadened to Gram negative targets.

An assessment of the influence of the industry distribution chain on the oxygen levels in commercial modified atmosphere packaged cheddar cheese using non-destructive oxygen sensor technology

The establishment and control of oxygen levels in packs of oxygen-sensitive food products such as cheese is imperative in order to maintain product quality over a determined shelf life. Oxygen sensors quantify oxygen concentrations within packaging using a reversible optical measurement process, and this non-destructive nature ensures the entire supply chain can be monitored and can assist in pinpointing negative issues pertaining to product packaging. This study was carried out in a commercial cheese packaging plant and involved the insertion of 768 sensors into 384 flow-wrapped cheese packs (two sensors per pack) that were flushed with 100% carbon dioxide prior to sealing. The cheese blocks were randomly assigned to two different storage groups to assess the effects of package quality, packaging process efficiency, and handling and distribution on package containment. Results demonstrated that oxygen levels increased in both experimental groups examined over the 30-day assessment period. The group subjected to a simulated industrial distribution route and handling procedures of commercial retailed cheese exhibited the highest level of oxygen detected on every day examined and experienced the highest rate of package failure. The study concluded that fluctuating storage conditions, product movement associated with distribution activities, and the possible presence of cheese-derived contaminants such as calcium lactate crystals were chief contributors to package failure.