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.

The life history and ecology of black scabbardfish (Aphanopus carbo Lowe 1839) in the north-east Atlantic

The black scabbardfish is a deep water species that supports commercial fisheries across a large area of the NE Atlantic shelf. The life history of black scabbardfish is poorly understood and a major unresolved issue is population structure. In this study it was used a combination of methodologies to get further knowledge in the life history and population structure of A. carbo over its wide distribution range in the Northeast Atlantic. The new knowledge acquired during this study, will increase our ability to better manage this species in the NE Atlantic. It has been postulated that fish caught to the west of the British Isles are pre-adults that migrate further south (to Madeira) for spawning, implying a single panmictic population. In this study, specimens of Aphanopus carbo were sampled between September 2008 and May 2010 from two different areas: NW Scotland (French trawlers and deep water surveys) and Madeira Islands (longliners commercial landings). Geographical differences in reproductive state of scabbardfish were evident, supportive of a north-south migration theory. In the northern area, all specimens found were immature, while in Madeira all maturity stages were observed. In Madeira, spawning occurred during the fourth quarter, with peak maturity in October (males) and in November (females). The age of this species has proven difficult and has led to different and contradictory age and growth estimates. For this study, we used two reading interpretations to determine age and estimate the growth parameters. To the west of the British Isles, specimens reached a lower maximum age and had a higher growth rate than those caught off Madeira. These differences are consistent with the theory of a single population of black scabbardfish in the NE Atlantic, highly segregate, with smaller, immature and younger fish caught to the west of the British Isles and bigger and mature caught in Madeira Islands. The feeding ecology showed strong evidence that the diet of black scabbardfish is associated with the spawning migration of blue whiting, which may support a northerly feeding migration theory for black scabbardfish. The stable isotope analyses in the muscle of black scabbardfish identified that black scabbardfish feeds on species with epipelagic and benthopelagic affinities. Comparison with stable isotope analysis in Madeira samples indicated that black scabbardfish feed at a similar trophic level and has the same trophic niche width in both areas, assuming similar baseline isotope compositions. Otolith stable isotopes (oxygen - δ18O and nitrogen - δ15N) analyses were used as a tool to clarify migratory behaviour. Otolith isotope ratios can provide insight into whether adults caught around Madeira fed in an isotopically depleted northerly ecosystem (NW Scotland) during their pre-adult period and then migrate towards south to spawn. Overall, the results support a south-north migration of pre adult fish from spawning areas around Madeira and a north-south migration from the west of Scotland to the spawning areas. Given its life cycle there is an urgent need that the management process recognizes the existence of a continuous widely distributed stock of black scabbardfish between the west of the British Isles and Madeira. The results highlight large scale dispersal in this species which needs to be treated as a highly migratory species and be managed as a single population.

Leveraging lessons learned in organizations through implementing practice-based organizational learning and performance improvement - An opportunity for context-based intelligent assistant support (CIAS)

Organizations that leverage lessons learned from their experience in the practice of complex real-world activities are faced with five difficult problems. First, how to represent the learning situation in a recognizable way. Second, how to represent what was actually done in terms of repeatable actions. Third, how to assess performance taking account of the particular circumstances. Fourth, how to abstract lessons learned that are re-usable on future occasions. Fifth, how to determine whether to pursue practice maturity or strategic relevance of activities. Here, organizational learning and performance improvement are investigated in a field study using the Context-based Intelligent Assistant Support (CIAS) approach. A new conceptual framework for practice-based organizational learning and performance improvement is presented that supports researchers and practitioners address the problems evoked and contributes to a practice-based approach to activity management. The novelty of the research lies in the simultaneous study of the different levels involved in the activity. Route selection in light rail infrastructure projects involves practices at both the strategic and operational levels; it is part managerial/political and part engineering. Aspectual comparison of practices represented in Contextual Graphs constitutes a new approach to the selection of Key Performance Indicators (KPIs). This approach is free from causality assumptions and forms the basis of a new approach to practice-based organizational learning and performance improvement. The evolution of practices in contextual graphs is shown to be an objective and measurable expression of organizational learning. This diachronic representation is interpreted using a practice-based organizational learning novelty typology. This dissertation shows how lessons learned when effectively leveraged by an organization lead to practice maturity. The practice maturity level of an activity in combination with an assessment of an activity’s strategic relevance can be used by management to prioritize improvement effort.

IS capability assessment - the MIND canvas

With the increasing ubiquity and growing pervasiveness of Information Systems (IS) in todays’ organisations, one of the capabilities of essential value to an organisation is its IS/IT (henceforth IS) capability. However, despite this increasing importance of the IS capability, research has barely focused on providing a measure for assessing the IT capability of an organization. In overview, IS capability has contributed significantly in understanding how information technology remains a valuable component of any modern day firm (Bharadwaj 2000, Santhanam and Hartono 2003). While these prior research focus in itself is of value in establishing the importance of IS capability, this current study posits that this research area is attaining maturity and it is about time we extend this stream to provide a measure for assessing and evaluating the IS capability that defines an organization. To borrow a quote from Peter Drucker - “if it can be measured; it can be improved”.