Principles and prejudice: The erosion of fairness in admissibility determinations relating to historic child sexual abuse trials in Ireland

This thesis interrogates the construction of fairness to the accused in historic child sexual abuse trials in Ireland. The protection of fairness is a requirement of any trial that claims to adhere to the rule of law. Historic child sexual abuse trials, in which the charges relate to events that are alleged to have taken place decades previously, present serious challenges to the ability of the trial process to safeguard fairness. They are a litmus test of the courts’ commitment to fairness. The thesis finds that in historic abuse trials fairness to the accused has been significantly eroded and that therefore the Irish Courts have failed to respect the core of the rule of law in these most serious of prosecutions. The thesis scrutinises two bodies of case law, both of which deal with the issue of whether evidence should reach the jury. First, it examines the decisions on applications brought by defendants seeking to prohibit their trial. The courts hearing prohibition applications face a dilemma: how to ensure the defendant is not put at risk of an unfair trial, while at the same time recognising that delay in reporting is a defining feature of these cases. The thesis traces the development of the prohibition case law and tracks the shifting interpretations given to fairness by the courts. Second, the thesis examines what fairness means in the superior courts’ decisions regarding the admissibility of the following kinds of evidence, each of which presents particular challenges to the ability of the trial to safeguard fairness: evidence of multiple complainants; evidence of recovered memories and evidence of complainants’ therapeutic records. The thesis finds that in both bodies of case law the Irish courts have hollowed out the meaning of fairness. It makes proposals on how fairness might be placed at the heart of courts’ decisions on admissibility in historic abuse trials. The thesis concludes that the erosion of fairness in historic abuse trials is indicative of a move away from the liberal model of criminal justice. It cautions that unless fairness is prioritised in historic child sexual abuse trials the legitimacy of these trials and that of all Irish criminal trials will be contestable.

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.