This thesis is devoted to two specific types of risk: portfolio credit risk, which originates in the possibility that borrowers are not able to repay their debts as previously agreed upon, and systemic risk covering the risk of an entire financial system.The first part of this thesis focuses on portfolio credit risk. Starting with a credit portfolio with n counterparties and a structural definition of default, we develop the first top down first-passage model for portfolio credit risk.Structural variables in our model are the portfolio asset value process modeled by a time changed geometric Brownian motion and time independent sequential default barriers. The i-th default occurs if the portfolio asset value process hits the i-th barrier.In order to obtain a tractable model, we study different incomplete information approaches with different assumptions on the availability of information. We derive reduced form formulas for prices of credit sensitive securities and provide an algorithm to simulate the default times. Due to the specific time change which itself depends on the default times, our model has the flexibility to model contagion effects.The second part of this thesis is devoted to systemic risk measurement from the perspective of a financial regulator. Here, we generalize a recent axiomatic approach in several ways:We work on a general probability space and our main objects of interest are convex, not necessarily positively homogeneous, systemic risk measures. These can be decomposed into a convex single-firm risk measure and a convex aggregation function determining how to pool the losses of the individual firms contained in the underlying financial system. Based on this decomposition, we obtain different representation results for convex systemic risk measures, and as an important application of the dual representation, we discuss an appropriate risk attribution method.Eventually, we develop the first dynamic approach to systemic risk by studying conditional and dynamic systemic risk measures for multi-dimensional bounded discrete time processes. We are able to extend our decomposition and representation results to this setting. In order to answer the question of how conditional systemic risk measures at different points in time depend on each other, we finally introduce and discuss an appropriate notion of time-consistency for dynamic systemic risk measures and their components.
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