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.

Model and visualise the relationship between energy consumption and temperature distribution in cold rooms

In the area of food and pharmacy cold storage, temperature distribution is considered as a key factor. Inappropriate distribution of temperature during the cooling process in cold rooms will cause the deterioration of the quality of products and therefore shorten their life-span. In practice, in order to maintain the distribution of temperature at an appropriate level, large amount of electrical energy has to be consumed to cool down the volume of space, based on the reading of a single temperature sensor placed in every cold room. However, it is not clear and visible that what is the change of energy consumption and temperature distribution over time. It lacks of effective tools to visualise such a phenomenon. In this poster, we initially present a solution which combines a visualisation tool with a Computational Fluid Dynamics (CFD) model together to enable users to explore such phenomenon.

The political and economic context of Keynes’s 1933 Finlay lecture: transforming a business practitioner’s ways of knowing

This thesis is structured in the format of a three part Portfolio of Exploration to facilitate transformation in my ways of knowing to enhance an experienced business practitioner’s capabilities and effectiveness. A key factor in my ways of knowing, as opposed to what I know, is my exploration of context and assumptions. By interacting with my cultural, intellectual, economic, and social history, I seek to become critically aware of the biographical, historical, and cultural context of my beliefs and feelings about myself. This Portfolio is not exclusively for historians of economics or historians of ideas but also for those interested in becoming more aware of how these culturally assimilated frames of reference and bundles of assumptions that influence the way they perceive, think, decide, feel and interpret their experiences in order to operate more effectively in their professional and organisational lives. In the first part of my Portfolio, I outline and reflect upon my Portfolio’s overarching theory of adult development; the writings of Harvard’s Robert Kegan and Columbia University’s Jack Mezirow. The second part delves further into how meaning-making, the activity of how one organises and makes sense of the world and how meaning-making evolves to different levels of complexity. I explore how past experience and our interpretations of history influences our understandings since all perception is inevitably tinged with bias and entrenched ‘theory-laden’ assumptions. In my third part, I explore the 1933 inaugural University College Dublin Finlay Lecture delivered by economist John Maynard Keynes. My findings provide a new perspective and understanding of Keynes’s 1933 lecture by not solely reading or relying upon the text of the three contextualised essay versions of his lecture. The purpose and context of Keynes’s original longer lecture version was quite different to the three shorter essay versions published for the American, British and German audiences.