Systemic risk is the risk that an economic shock may result in the breakdown of the fundamental functions of the financial system. It can involve multiple vectors of infection such as chains of losses or consecutive failures of financial institutions that may ultimately cause the failure of the financial system to provide liquidity, stable prices, and to perform economic activities. This thesis develops methods to quantify systemic risk, its effect on the financial system and perhaps more importantly, to determine its cause. In the first chapter, we provide an overview and a literature review of the topics covered in this thesis. First, we present a literature review on network-based models of systemic risk. Finally we end the first chapter with a review on market impact models. In the second chapter, we consider one unregulated financial institution with constant absolute risk aversion investment risk preferences that optimizes its strategies in a multi asset market impact model with temporary and permanent impact. We prove the existence and derive explicitly the optimal trading strategies. Furthermore, we conduct numerical exploration on the sensitivity of the optimal trading curve. This chapter sets the foundation for further research into multi-agent models and systemic risk models with optimal behaviours. In the third chapter, we extend the market impact models to the multi-agent setting. The agents follow a game theoretic strategy that is constrained by the regulations imposed. Furthermore, the agents must liquidate themselves if they become insolvent or unable to meet the regulations imposed on them. This paper provides a bridge between market impact models and network models of systemic risk. In chapter four, we introduce a financial network model that combines the default and liquidity stress mechanisms into a ``double cascade mapping''. Unlike simpler models, this model can quantify how illiquidity or default of one bank influences the overall level of liquidity stress and default in the system. We derive large-network asymptotic cascade mapping formulas that can be used for efficient network computations of the double cascade. Finally we use systemic risk measures to compare the results of including with and without an asset firesale mechanism. / Thesis / Doctor of Philosophy (PhD)

Level crossing times and their applications in finance are of importance, given certain threshold levels that represent the "desirable" or "sell" values of a stock. In this thesis, we make use of Wald's lemmas and various deep results from renewal theory, in the context of finance, in modelling the growth of a portfolio of stocks. Several models are employed .