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.

People and place in the new frontier: an examination of Han and Uyghur ethnic identities

This thesis demonstrates how Han and Uyghur ethnic identities are constructed in urban Xinjiang, how they have evolved over time and how both identities gain their meaning largely from a process of interaction with the ‘other’. It shows that the boundaries that exist between Uyghur and Han hugely influence the identity content of both. Based on over 120 interviews carried out over 3 years, it brings a clear analytical framework and conceptual clarity to the questions of how ethnic identities are constructed and maintained in Xinjiang

Place, teenagers and urban identities: Growing up in the revanchist city

The recreational lives of teenagers in Ireland has been the subject of much debate in recent years. The subject has received much attention from academics, particularly in the UK and the US. In Ireland there is a dearth of research on, and a poor understanding of teenagers recreational lives. Additionally much of the research from the UK and the US to date has been focused on teenagers’ use of the street for recreation, arguing that teenagers are increasingly pushed out of public space. The research frequently emphasises teenagers’ resistance against adult hegemony. This thesis explores the recreational geographies of teenagers living in two socially and economically distinct neighbourhoods in Cork. It seeks to fill in gaps in knowledge of teenagers recreational lives in Ireland and contribute to geographical wisdom on teenagers’ geographies. Using a mixed method approach and a variety of thinking tools this research shows that teenagers living in Cork are growing up in a revanchist society. The thesis demonstrates how teenagers’ recreational practices are currently being configured in Irish society, unfolding strategies of dominance and affection which construct and regulate the recreational lives of teenagers. The effects of revanchism on teenagers’ experiences of outdoor space for recreation are also pursued. Furthermore the socio-spatial contingencies of teenagers’ recreational lives and revanchism are probed throughout the thesis, but in greater depth in the final chapters. The work also addresses an under-researched aspect of young people’s recreational - relationships with pets. Lastly, the subject of teenagers’ right to urban space is critically analysed.

The geographies of encounter: investigating the spatiality and construction of 'meaningful' encounters with difference through the experiences of international students at University College Cork, Ireland

The purpose of this research is to investigate how international students negotiate encounters with Irish students and construct ‘meaning’ from those encounters in the spaces of the university and city. As cities are increasingly characterised by a multiplexity of diversity, the issue of living with difference is becoming more and more pertinent. In the wake of escalating socio-spatial polarisation, inter-cultural tension, racism, and xenophobia, the geographies of encounter seek to untangle the interactions that occur in the quotidian activities and spaces of everyday life to determine whether such encounters might reduce prejudice, antipathy and indifference and establish common social bonds (Amin 2002; Valentine 2008). Thus far, the literature has investigated a number of sites of encounter; public space, the home, neighbourhoods, schools, sports clubs, public transport, cafes and libraries (Wilson 2011; Schuermans 2013; Hemming 2011; Neal and Vincent 2011; Mayblin, Valentine and Anderrson 2015; Laurier and Philo 2006; Valentine and Sadgrove 2013; Harris, Valentine and Piekut 2014; Fincher and Iveson 2008). While these spaces produce a range of outcomes, the literature remains frustrated by a lack of clarity of what constitutes a ‘meaningful’ encounter and how such encounters might be planned for. Drawing on survey and interview data with full-time international students at University College Cork, Ireland, this study contributes to understanding how encounters are shaped by the construction and reproduction of particular identities in particular spaces, imbuing spaces with uneven power frameworks that produce diverse outcomes. Rather than identifying a singular ‘meaningful’ outcome of encounter as a potential panacea to the issues of exclusion and oppression, the contention here is to recognise a range of outcomes that are created by individuals in a range of ways. To define one outcome of encounter as ‘meaningful’ is to overlook the scale of intensity of diverse interactions and the multiplicity of ways in which people learn to live with difference.

"On our way": identities and representations of African women seeking asylum in Ireland

This thesis provides the first explicit Postcolonial study of asylum in the Irish context that integrates Black Feminist analyses of intersectional identity with Postcolonial Feminist theories of representation. African women seeking asylum in the Republic of Ireland were key political instruments used by the state to re-draw racial lines. The study examines how, for a group of African women “On their Way” through asylum, identity and representation work hand in hand to force identities, subaltern spaces and bodies to occupy them. Rich biographical data is gathered through mixed art and drama methods over two intensive participatory research projects conducted in a small Irish city. Data analysis critically examines the poetics (practices that signify) and politics (the powers that govern these practices) and affective economies of global and local NGO visual representations, exposing how they consume, fragment, and appropriate African women’s identities and bodies. Though hypervisible, the women themselves “cannot speak”. The women in the study reported feeling “tired” and “used”. Asking “What work are they doing as they do asylum?” the study finds that black female identities and bodies are forced to perform political, cultural, emotional and material labour on their way through this context of Irish asylum. The author argues that Postcolonial Asylum is a performative encounter that re-scripts colonial race/class/gender discourse through a humanitarian alibi to naturalize European/white supremacy, reinscribe patriarchal power and justify racialised incarceration of bodies seeking asylum in the North. This study takes an interdisciplinary approach that centralizes Black and Postcolonial Feminist theory and innovates Participatory Art-Based Action methodology. Black and Postcolonial feminisms can recognize, theorize and replenish black female political and intellectual agency. Participatory Action research, if grounded in Black feminist epistemology and ethics, can allow participants to “speak back” to what is already said about them in spaces of convivial self-representation.