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.

System operational costs reduction with non-conventional reactive power sources

Wind energy installations are increasing in power systems worldwide and wind generation capacity tends to be located some distance from load centers. A conflict may arise at times of high wind generation when it becomes necessary to curtail wind energy in order to maintain conventional generators on-line for the provision of voltage control support at load centers. Using the island of Ireland as a case study and presenting commercially available reactive power support devices as possible solutions to the voltage control problems in urban areas, this paper explores the reduction in total generation costs resulting from the relaxation of the operational constraints requiring conventional generators to be kept on-line near load centers for reactive power support. The paper shows that by 2020 there will be possible savings of 87€m per annum and a reduction in wind curtailment of more than a percentage point if measures are taken to relax these constraints.

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.

Enhancing non-refractory aerosol apportionment from an urban industrial site through receptor modelling of complete high time-resolution aerosol mass spectra

Receptor modelling was performed on quadrupole unit mass resolution aerosol mass spectrometer (Q-AMS) sub-micron particulate matter (PM) chemical speciation measurements from Windsor, Ontario, an industrial city situated across the Detroit River from Detroit, Michigan. Aerosol and trace gas measurements were collected on board Environment Canada’s CRUISER mobile laboratory. Positive matrix factorization (PMF) was performed on the AMS full particle-phase mass spectrum (PMFFull MS) encompassing both organic and inorganic components. This approach was compared to the more common method of analysing only the organic mass spectra (PMFOrg MS). PMF of the full mass spectrum revealed that variability in the non-refractory sub-micron aerosol concentration and composition was best explained by six factors: an amine-containing factor (Amine); an ammonium sulphate and oxygenated organic aerosol containing factor (Sulphate-OA); an ammonium nitrate and oxygenated organic aerosol containing factor (Nitrate-OA); an ammonium chloride containing factor (Chloride); a hydrocarbon like organic aerosol (HOA) factor; and a moderately oxygenated organic aerosol factor (OOA). PMF of the organic mass spectrum revealed three factors of similar composition to some of those revealed through PMFFull MS: Amine, HOA and OOA. Including both the inorganic and organic mass proved to be a beneficial approach to analysing the unit mass resolution AMS data for several reasons. First, it provided a method for potentially calculating more accurate sub-micron PM mass concentrations, particularly when unusual factors are present, in this case, an Amine factor. As this method does not rely on a priori knowledge of chemical species, it circumvents the need for any adjustments to the traditional AMS species fragmentation patterns to account for atypical species, and can thus lead to more complete factor profiles. It is expected that this method would be even more useful for HR-ToF-AMS data, due to the ability to better understand the chemical nature of atypical factors from high resolution mass spectra. Second, utilizing PMF to extract factors containing inorganic species allowed for the determination of extent of neutralization, which could have implications for aerosol parameterization. Third, subtler differences in organic aerosol components were resolved through the incorporation of inorganic mass into the PMF matrix. The additional temporal features provided by the inorganic aerosol components allowed for the resolution of more types of oxygenated organic aerosol than could be reliably re-solved from PMF of organics alone. Comparison of findings from the PMFFull MS and PMFOrg MS methods showed that for the Windsor airshed, the PMFFull MS method enabled additional conclusions to be drawn in terms of aerosol sources and chemical processes. While performing PMFOrg MS can provide important distinctions between types of organic aerosol, it is shown that including inorganic species in the PMF analysis can permit further apportionment of organics for unit mass resolution AMS mass spectra.

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.