Building effectiveness communication ratios (BECs): an integrated ‘life-cycle’ methodology for mitigating energy-use in buildings

Current building regulations are generally prescriptive in nature. It is widely accepted in Europe that this form of building regulation is stifling technological innovation and leading to inadequate energy efficiency in the building stock. This has increased the motivation to move design practices towards a more ‘performance-based’ model in order to mitigate inflated levels of energy-use consumed by the building stock. A performance based model assesses the interaction of all building elements and the resulting impact on holistic building energy-use. However, this is a nebulous task due to building energy-use being affected by a myriad of heterogeneous agents. Accordingly, it is imperative that appropriate methods, tools and technologies are employed for energy prediction, measurement and evaluation throughout the project’s life cycle. This research also considers that it is imperative that the data is universally accessible by all stakeholders. The use of a centrally based product model for exchange of building information is explored. This research describes the development and implementation of a new building energy-use performance assessment methodology. Termed the Building Effectiveness Communications ratios (BECs) methodology, this performance-based framework is capable of translating complex definitions of sustainability for energy efficiency and depicting universally understandable views at all stage of the Building Life Cycle (BLC) to the project’s stakeholders. The enabling yardsticks of building energy-use performance, termed Ir and Pr, provide continuous design and operations feedback in order to aid the building’s decision makers. Utilised effectively, the methodology is capable of delivering quality assurance throughout the BLC by providing project teams with quantitative measurement of energy efficiency. Armed with these superior enabling tools for project stakeholder communication, it is envisaged that project teams will be better placed to augment a knowledge base and generate more efficient additions to the building stock.

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.