In this thesis, we are interested in the asymptotic analysis of extremes and risks. The heavy-tailed distribution function is used to model the extreme risks, which is widely applied in insurance and is gradually penetrating in finance as well. We also use various tools such as copula, to model dependence structures, and extreme value theorem, to model rare events. We focus on modelling and analysing of extreme risks as well as demonstrate how the derived results that can be used in practice. We start from a discrete-time risk model. More concretely, consider a discrete-time annuity-immediate risk model in which the insurer is allowed to invest its wealth into a risk-free or a risky portfolio under a certain regulation. Then the insurer is said to be exposed to a stochastic economic environment that contains two kinds of risk, the insurance risk and financial risk. The former is traditional liability risk caused by insurance loss while the latter is the asset risk resulting from investment. Within each period, the insurance risk is denoted by a real-valued random variable X, and the financial risk Y as a positive random variable fulfils some constraints. We are interested in the ruin probability and the tail behaviour of maximum of the stochastic present values of aggregate net loss with Sarmanov or Farlie-Gumbel-Morgenstern (FGM) dependent insurance and financial risks. We derive asymptotic formulas for the finite-ruin probability with lighted-tailed or moderately heavy-tailed insurance risk for both risk-free investment and risky investment. As an extension, we improve the result for extreme risks arising from a rare event, combining simulation with asymptotics, to compute the ruin probability more efficiently. Next, we consider a similar risk model but a special case that insurance and financial risks following the least risky FGM dependence structure with heavy-tailed distribution. We follow the study of Chen (2011) that the finite-time ruin probability in a discrete-time risk model in which insurance and financial risks form a sequence of independent and identically distributed random pairs following a common bivariate FGM distribution function with parameter -1 ≤ θ ≤ 1 governing the strength of dependence. For the subexponential case, when -1 < θ ≤ 1, a general asymptotic formula for the finite-time ruin probability was derived. However, the derivation there is not valid for θ = -1. In this thesis, we complete the study by extending Chen's work to θ = -1 that the insurance risk and financial risk are negatively dependent. We refer this situation as the least risky FGM dependent insurance risk and financial risk. The new formulas for θ = −1 look very different from, but are intrinsically consistent with, the existing one for -1 < θ ≤ 1, and they offer a quantitative understanding on how significantly the asymptotic ruin probability decreases when θ switches from its normal range to its negative extremum. Finally, we study a continuous-time risk model. Specifically, we consider a renewal risk model with a constant premium and a constant force of interest rate, where the claim sizes and inter-arrival times follow certain dependence structures via some restriction on their copula function. The infinite-time absolute ruin probabilities are studied instead of the traditional infinite-time ruin probability with light-tailed or moderately heavy-tailed claim-size. Under the assumption that the distribution of the claim-size belongs to the intersection of the convolution-equivalent class and the rapid-varying tailed class, or a larger intersection class of O-subexponential distribution, the generalized exponential class and the rapid-varying tailed class, the infinite-time absolute ruin probabilities are derived.

Since the Global Financial Crisis, the literature of financial networks analysis has been trying to investigate the changes in the financial networks structure, that led to the instability of the financial system. The Global Financial Crisis followed by the Great Recession costed taxpayers an unprecedented $14 trillion (Alessandri and Haldane, 2009), austerity and downturns in GDP. The dynamics of the financial networks transferred the collapse of a US housing market bubble into a large meltdown of the financial systems globally. The study of systemic risk and macro-prudential policy has come to the forefront to model and manage the negative externalities of monetary, fiscal and financial sector activities that can lead to system wide instabilities and failure. The dimensions of crisis propagation have been modelled as those that can spread cross-sectionally in domino like failures with global scope, or build up over time, as in asset bubbles. The cross sectional propagation of shocks that occur due to non-payment of debt or other financial obligations with the failure of a financial intermediary or a sovereign leading to the failure of other economic entities, is called financial contagion. Cross sectional analysis of financial contagion can be done using statistical methods or by network analysis. The latter gives a structural model of the interconnections in terms of financial obligations. This dissertation uses both approaches to model financial contagion. The applications include the study of systemic risk in Eurozone Sovereign crisis, the US CDS market and the global banking network. This is organized in three self-contained chapters Our contribution to the literature begins with the study of the dynamics of the market of the Credit Default Swap (CDS) contracts for selected Eurozone sovereigns and the UK. The EWMA correlation analysis and the Granger-causality test demonstrate that there was contagion effect since correlations and cross-county interdependencies increased after August 2007. Furthermore, the IRF analysis shows that among PIIGS, the CDS spreads of Spain and Ireland have the biggest impact on the European CDS spreads, whereas the UK is found not be a source of sovereign contagion to the Eurozone. Next we perform the empirical reconstruction of the US CDS network based on the real-world data obtained from the FDIC Call Reports, and study the propagation of contagion, assuming different network structures. The financial network shows a highly tiered core-periphery structure. We find that network topology matters for the stability of the financial system. The “too interconnected to fail” phenomenon is discussed and shown to be the result of highly tiered network with central core of so called super-spreaders. In this type of network the contagion is found to be short, without multiple waves, but with very high losses brought by the core of the network. Finally we study a global banking network (GBN) model based on the Markose (2012) eigen-pair approach and propose a systemic risk indices (SRI) which provide early warning signals for systemic instability and also the rank order of the systemic importance and vulnerability of the banking systems. The empirical model is based on BIS Consolidated Banking Statistics for the exposures of 19 national banking systems to the same number of debtor countries and the data obtained from Bankscope for the equity capital of these 19 national banking systems. The SRI is based on the ratio of the netted cross-border exposures of the national banking systems to their respective equity capital. The eigen-pair method stipulates that if the maximum eigenvalue of the network exceeds the capital threshold, there is cause for concern of a contagion. This is compared with the loss multiplier SRI proposed by Castrén and Rancan (2012). The latter is found to have no early warning capabilities and peaks well after the onset of the crisis in 2009 while the eigen-pair SRI gives ample warning by late 2006 that the cross border liabilities was unsustainable in respect of the equity capital of the national banking systems. We contribute to the literature by highlighting the efficacy of the network approach to systemic stability analysis of GBNs. In particular we develop an eigen-pair approach for GBNs and prove its usefulness in an early warning context.

The primary aim, as set out in the Introduction, is to explore women’s specific difficulties regarding labour market outcomes in the first decade of the 21st century, related to their dual role as mothers and labour force participants. The overarching context of the thesis is a contemporary profile of the working woman in Great Britain who is struggling to balance motherhood and paid work successfully, with the consequences this might have for her mental health. This thesis contains three empirical chapters exploring women’s employment and health interactions, through the consequences of the 2008/9 economic crisis on the UK gender wage gap, the effects of postpartum depression on maternal employment after childbirth, and the potential long-term impacts of postpartum depression on children’s emotional health and cognitive developmental outcomes. Specifically, this thesis seeks to address the following research questions: Did the great recession affect the wage gender gap? Does postpartum depression affect employment? Does postpartum depression predict emotional and cognitive difficulties in 11 year olds? Recent estimates reveal that 1 in 10 children aged 5-16 years have a diagnosable mental health problem and 1 in 5 mothers suffer from perinatal mental disorders, which highlight how widespread mental health problems are and how important the promotion of good mental health and prevention is at crucial stages in development. The results of the three empirical chapters of the thesis point to the need for an innovative and comprehensive approach to the distinct problems faced by different groups and sub-categories within the population.

Finance should be studied as a hard science, where scientific methods apply. When a trading strategy is proposed, the underlying model should be transparent and defined robustly to allow other researchers to understand and examine it thoroughly. Any reports on experimental results must allow other researchers to trace back to the original data and models that produced them. Like any hard sciences, results must be repeatable to allow researchers to collaborate and build upon each other’s results. Large-scale collaboration, when applying the steps of scientific investigation, is an efficient way to leverage crowd science to accelerate research in finance. Unfortunately, the current reality is far from that. Evidence shows that current methods of investigation in finance in most cases do not allow for reproducible and falsifiable procedures of scientific investigation. As a consequence, the majority of financial decisions at all levels, from personal investment choices to overreaching global economic policies, rely on some variation of try-and-error and are mostly non-scientific by definition. We lack transparency for procedures and evidence, proper explanation of market events, predictability on effects, or identification of causes. There is no clear demarcation of what is inherently scientific, and as a consequence, the line between fake and true is blurred. In this research, we advocate the use of a next-generation investigative approach leveraging forces of human diversity, micro-specialized crowds, and proper computer-assisted control methods associated with accessibility, reproducibility, communication, and collaboration. This thesis is structured in three distinctive parts. The first part defines a set of very specific cognitive and non-cognitive enablers for crowd-based scientific investigation: methods of proof, large-scale collaboration, and a domain-specific computational representation. These enablers allow the application of procedures of structured scientific investigation powered by crowds, a “collective brain in which neurons are human collaborators”. The second part defines a specialized computational representation to allow proper controls and collaboration in large-scale in the field of economics. A computational representation is a role-based representation system based on facets, contributions, and constraints of data, and used to define concepts related to a specific domain of knowledge for crowd-based investigation. The third and last part performs an end-to-end investigation of a non-trivial problem in finance by measuring the actual performance of a momentum strategy in technical analysis, applying formal methods of investigation developed over the first and second part of this research.